A347868 - OEIS

A347868

Number of partitions of n such that 4*(greatest part) >= (number of parts).

1, 2, 3, 5, 6, 10, 14, 21, 29, 40, 53, 73, 96, 129, 168, 221, 284, 369, 471, 603, 763, 966, 1211, 1521, 1892, 2355, 2912, 3600, 4423, 5434, 6639, 8107, 9855, 11968, 14476, 17495, 21067, 25342, 30393, 36406, 43489, 51891, 61761, 73421, 87087, 103172, 121977, 144045, 169780, 199883

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OFFSET

1,2

COMMENTS

Also, the number of partitions of n such that (greatest part) <= 4*(number of parts).

LINKS

Table of n, a(n) for n=1..50.

FORMULA

G.f.: Sum_{k>=1} x^k * Product_{j=1..k} (1-x^(4*k+j-1))/(1-x^j).

PROG

(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k*prod(j=1, k, (1-x^(4*k+j-1))/(1-x^j))))

CROSSREFS