Search: id:A028338
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%I A028338
%S A028338 1,1,1,3,4,1,15,23,9,1,105,176,86,16,1,945,1689,950,230,25,1,10395,
%T A028338 19524,12139,3480,505,36,1,135135,264207,177331,57379,10045,973,49,
%U A028338 1,2027025,4098240,2924172,1038016,208054,24640,1708,64,1,34459425
%N A028338 Triangle of coefficients in expansion of (x+1)(x+3)...(x+2n-1).
%C A028338 Row sums are A000165. [From Paul Barry (pbarry(AT)wit.ie), Feb 07 2009]
%H A028338 T. D. Noe, <a href="b028338.txt">Rows n=0..50 of triangle, flattened</
               a>
%F A028338 Triangle T(n, k), read by rows, given by [1, 2, 3, 4, 5, 6, 7, ...] DELTA 
               [1, 0, 1, 0, 1, 0, 1, 0, ...] where DELTA is the operator defined 
               in A084938 . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 20 
               2005
%F A028338 T(n, k) = sum[(-2)^(n-i) binomial(i, k) s(n, i), i=k..n] where s(n, k) 
               are signed Stirling numbers of the first kind. - Francis Woodhouse 
               (fwoodhouse(AT)gmail.com), Nov 18 2005
%F A028338 G.f.: G.f.: 1/(1-(x+xy)/(1-2x/(1-(3x+xy)/(1-4x/(1-(5x+xy)/(1-6xy/(1-... 
               (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Feb 07 
               2009]
%F A028338 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 
               2009: (Start)
%F A028338 a(n, m) = (2*n-1)*a(n-1,m)+a(n-1,m-1) with a(n, 0) = (2*n-1)!! and a(n, 
               n) = 1.
%F A028338 (End)
%e A028338 E.g. For n=4, (x + 1) (x + 3) (x + 5) (x + 7) = x^4+16*x^3+86*x^2+176*x+105
%e A028338 1; 1,1; 3,4,1; 15,23,9,1; 105,176,86,16,1; ...
%p A028338 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 
               2009: (Start)
%p A028338 nmax:=8; mmax:=nmax: for n from 0 to nmax do a(n,0):=doublefactorial(2*n-1) 
               od: for n from 0 to nmax do a(n,n):=1 od: for n from 2 to nmax do 
               for m from 1 to n-1 do a(n,m) := (2*n-1)*a(n-1,m)+a(n-1,m-1) od; 
               od: T:=0; for n from 0 to nmax do for m from 0 to n do a(T):=a(n,
               m); T:=T+1 od: od: seq(a(n),n=0..T-1);
%p A028338 (End)
%t A028338 T[n_, k_] := Sum[(-2)^(n-i) Binomial[i, k] StirlingS1[n, i], {i, k, n}] 
               (Woodhouse)
%Y A028338 A039757 is signed version.
%Y A028338 Diagonals : A001147, A004041, A028339, A028340, A028341; A000012, A000290, 
               A024196, A024197, A024198. Row sums : A000165
%Y A028338 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 08 
               2009: (Start)
%Y A028338 A161198 is a scaled triangle version and A109692 is a transposed triangle 
               version.
%Y A028338 (End)
%Y A028338 Sequence in context: A114189 A059110 A100326 this_sequence A039757 A136228 
               A154829
%Y A028338 Adjacent sequences: A028335 A028336 A028337 this_sequence A028339 A028340 
               A028341
%K A028338 tabl,nonn,easy,nice
%O A028338 0,4
%A A028338 R. W. Gosper

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