A373070 Number of partitions of n such that (smallest part) >= 5*(number of parts).

1, 0, 0, 0, 0, 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, 15, 16, 17, 19, 20, 22, 24, 26, 28, 31, 33, 36, 39, 42, 45, 49, 52, 56, 60, 64, 68, 73, 77, 82, 87, 92, 97, 103, 108, 114, 120, 126, 132, 139, 145, 153, 160, 168, 176, 186, 194

Offset

0,21

Links

Table of n, a(n) for n=0..85.

Formula

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

Prog

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

Crossrefs

Cf. A003114, A373067, A373068, A373069.

Cf. A350899, A373076.

Sequence in context: A350899 A350898 A373076 * A330878 A373075 A350894

Adjacent sequences: A373067 A373068 A373069 * A373071 A373072 A373073

Keyword

nonn

Author

Seiichi Manyama, May 22 2024

Status

approved