Search: id:A000023
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%I A000023 M0373 N0140
%S A000023 1,1,2,2,8,8,112,656,5504,49024,491264,5401856,64826368,842734592,
%T A000023 11798300672,176974477312,2831591702528,48137058811904,866467058876416,
%U A000023 16462874118127616,329257482363600896,6914407129633521664,152116956851941670912,
               3498690007594650042368,83968560182271617794048,2099214004556790411296768,
               54579564118476550760824832,1473648231198866870408052736
%V A000023 1,-1,2,-2,8,8,112,656,5504,49024,491264,5401856,64826368,842734592,
%W A000023 11798300672,176974477312,2831591702528,48137058811904,866467058876416,
%X A000023 16462874118127616,329257482363600896,6914407129633521664,152116956851941670912,
               3498690007594650042368,83968560182271617794048,2099214004556790411296768,
               54579564118476550760824832,1473648231198866870408052736
%N A000023 E.g.f.: exp(-2*x)/(1-x).
%C A000023 A010843, A000023, A000166, A000142, A000522, A010842, A053486, A053487 
               are successive binomial transforms with the e.g.f. exp(k*x)/(1-x) 
               and recurrence b(n)=n*b(n-1)+k^n and are related to incomplete gamma 
               functions at k. In this case k=-2, a(n)=n*a(n-1)+(-2)^n.
%C A000023 GAMMA(n+1,k)*exp(k) = Sum_{i=0..n} (-1)^(n-i)*binomial(n,i)*i^(n-i)*(i+k)^i. 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 19 2002
%C A000023 a(n) is the permanent of the n X n matrix with -1's on the diagonal and 
               1's elsewhere . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 
               15 2003
%D A000023 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000023 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000023 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               210.
%H A000023 T. D. Noe, <a href="b000023.txt">Table of n, a(n) for n=0..100</a>
%H A000023 A. R. Kr\"auter, <a href="http://www.mat.univie.ac.at/~slc/opapers/s09kraeu.html">
               Permanenten - Ein kurzer \"Uberblick</a>
%H A000023 A. R. Kr\"auter, <a href="http://www.mat.univie.ac.at/~slc/opapers/s11kraeu.html">
               \"Uber die Permanente gewisser zirkul\"arer Matrizen...</a>
%H A000023 S. Plouffe, <a href="http://www.lacim.uqam.ca/~plouffe/OEIS/b000023.txt">
               Table for n=0..2429</a>
%F A000023 a(n) = Sum(k=0..n, A008290(n, k)*(-1)^k ). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               Dec 15 2003
%F A000023 a(n)=sum{k=0..n, (-2)^(n-k)n!/(n-k)!}=sum{k=0..n, binomial(n, k)k!(-2)^(n-k)} 
               - Paul Barry (pbarry(AT)wit.ie), Aug 26 2004
%F A000023 a(n)=sum_{i=0..n} A008290(i)(-1)^i. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), 
               Jan 27 2008
%F A000023 a(n) = abs( exp(-2)*GAMMA(n+1,-2) ) (incomplete Gamma function) [From 
               Mark van Hoeij (hoeij(AT)math.fsu.edu), Nov 11 2009]
%p A000023 a:=n->n!*sum(((-2)^(k)/k!), k=0..n): seq(a(n), n=0..27); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2007
%o A000023 (PARI) a(n)=if(n<0,0,n!*polcoeff(exp(-2*x+x*O(x^n))/(1-x),n))
%Y A000023 Cf. A087891, A008290 A089258.
%Y A000023 Sequence in context: A037223 A066988 A100384 this_sequence A010584 A131659 
               A137726
%Y A000023 Adjacent sequences: A000020 A000021 A000022 this_sequence A000024 A000025 
               A000026
%K A000023 sign,new
%O A000023 0,3
%A A000023 N. J. A. Sloane (njas(AT)research.att.com).

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