A005116 Number of protruded partitions of n with largest part at most 10. (Formerly M2571)

1, 3, 6, 13, 25, 50, 94, 178, 328, 601, 1083, 1940, 3436, 6047, 10558, 18326, 31614, 54265, 92683, 157626, 266985, 450580, 757851, 1270757, 2124721, 3543318, 5894831, 9785243, 16210036, 26802756, 44240560, 72906608, 119969779

Offset

1,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. P. Stanley, Ordered structures and partitions, Memoirs of the Amer. Math. Soc., no. 119 (1972).

Links

Table of n, a(n) for n=1..33.

R. P. Stanley, A Fibonacci lattice, Fib. Quart., 13 (1975), 215-232.

R. P. Stanley, Letter to N. J. A. Sloane, c. 1991

Formula

G.f.: (1-x)^10/Product(1-x-x^i+x^(1+2*i), i=1..10)-1. - Emeric Deutsch, Dec 19 2004

Maple

G:=(1-x)^10/Product(1-x-x^i+x^(1+2*i), i=1..10)-1: Gser:=series(G, x=0, 39): seq(coeff(Gser, x^n), n=1..37); # Emeric Deutsch, Dec 19 2004

Crossrefs

Sequence in context: A324129 A005406 A005407 * A121349 A215984 A074890

Adjacent sequences: A005113 A005114 A005115 * A005117 A005118 A005119

Keyword

nonn

Author

N. J. A. Sloane and Richard Stanley

Extensions

More terms from Emeric Deutsch, Dec 19 2004

Status

approved