A373076 Number of partitions of n such that (smallest part) > 5*(number of parts).

1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 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, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 16, 16, 18, 19, 21, 22, 25, 26, 29, 31, 34, 36, 40, 42, 46, 49, 53, 56, 61, 64, 69, 73, 78, 82, 88, 92, 98, 103, 109, 114, 121, 126, 133, 139, 146, 152, 161

Offset: 0

Author

Seiichi Manyama, May 22 2024

Keywords

• nonn

Comments

This sequence is different from A350898.

Crossrefs

Cf. A003106, A373073, A373074, A373075.

Cf. A350899, A373070.

Programs

Mathematica

Join[{1},Table[Count[IntegerPartitions[n],?(#[[-1]]>5Length[#]&)],{n,90}]] (* _Harvey P. Dale, May 24 2025 *)

PARI

my(N=90, x='x+O('x^N)); Vec(sum(k=0, N, x^(5*k^2+k)/prod(j=1, k, 1-x^j)))

Formula

G.f.: Sum_{k>=0} x^(5*k^2+k)/Product_{j=1..k} (1-x^j).