A117953 - OEIS

A117953

Number of partitions of n into odd parts and such that parts having size k occur at most k times.

1, 1, 0, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 7, 8, 9, 10, 12, 14, 16, 19, 21, 24, 28, 32, 36, 41, 47, 53, 59, 67, 76, 85, 96, 108, 121, 135, 151, 169, 188, 210, 235, 261, 289, 322, 357, 395, 438, 485, 536, 592, 654, 721, 795, 876, 963, 1059, 1165, 1279, 1405, 1541, 1688, 1851

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OFFSET

0,7

LINKS

Table of n, a(n) for n=0..63.

FORMULA

G.f.=product((1-x^(2k(2k-1)))/(1-x^(2k-1)), k=1..infinity).

EXAMPLE

a(10)=4 because we have [9,1],[7,3],[5,5] and [3,3,3,1].

MAPLE

g:=product((1-x^(2*k*(2*k-1)))/(1-x^(2*k-1)), k=1..50): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..67);

CROSSREFS