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Search: id:A005380
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| A005380 |
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Number of partitions of n objects of 2 colors.
(Formerly M1601)
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+0
21
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| 1, 2, 6, 14, 33, 70, 149, 298, 591, 1132, 2139, 3948, 7199, 12894, 22836, 39894, 68982, 117948, 199852, 335426, 558429, 922112, 1511610, 2460208, 3977963, 6390942, 10206862, 16207444, 25596941, 40214896, 62868772, 97814358
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102; also in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89-102.
P. A. MacMahon, Memoir on symmetric functions of the roots of systems of equations, Phil. Trans. Royal Soc. London, 181 (1890), 481-536; Coll. Papers II, 32-87.
R. P. Stanley, Theory and application of plane partitions II, Studies in Appl. Math., 50 (1971), 259-279.
R. P. Stanley, Conjugate trace..., J. Combin. Theory, vol. A14 53-65 1973, esp. p. 64.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 7.99.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
N. J. A. Sloane, Transforms
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FORMULA
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G.f.: Product_{k=1..infinity} 1/(1-x^k)^(k+1). EULER transform of b(n) = n+1.
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MAPLE
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mul( (1-x^i)^(-i-1), i=1..80); series(%, x, 80); seriestolist(%);
with (numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:=etr (n-> n+1): seq (a(n), n=0..31); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]
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PROGRAM
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(PARI) a(n)=polcoeff(prod(i=1, n, (1-x^i+x*O(x^n))^-(i+1)), n)
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CROSSREFS
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Row sums of A060243. Cf. A000219.
Sequence in context: A110524 A083404 A089351 this_sequence A124612 A124613 A124614
Adjacent sequences: A005377 A005378 A005379 this_sequence A005381 A005382 A005383
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Christian G. Bower (bowerc(AT)usa.net), Sep 07 2002
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