A373074 - OEIS

A373074

Number of partitions of n such that (smallest part) > 3*(number of parts).

1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 11, 11, 13, 14, 16, 17, 20, 21, 24, 26, 29, 31, 35, 37, 41, 44, 48, 51, 56, 59, 64, 68, 74, 78, 85, 90, 98, 104, 113, 120, 131, 139, 151, 161, 175, 186, 202, 215, 233, 248, 268, 285, 308, 327, 352, 374, 402, 426, 457

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OFFSET

0,15

LINKS

Table of n, a(n) for n=0..78.

FORMULA

G.f.: Sum_{k>=0} x^(3*k^2+k)/Product_{j=1..k} (1-x^j).

MATHEMATICA

Join[{1}, Table[Count[IntegerPartitions[n], _?(#[[-1]]>3*Length[#]&)], {n, 80}]] (* Harvey P. Dale, Aug 15 2024 *)

PROG

(PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k^2+k)/prod(j=1, k, 1-x^j)))

CROSSREFS