A373075 Number of partitions of n such that (smallest part) > 4*(number of parts).

1, 0, 0, 0, 0, 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, 13, 14, 15, 17, 18, 20, 22, 24, 26, 29, 31, 34, 37, 40, 43, 47, 50, 54, 58, 62, 66, 71, 75, 80, 85, 90, 95, 101, 106, 113, 119, 126, 133, 142, 149, 159, 168, 179, 189, 202

Offset: 0

Author

Seiichi Manyama, May 22 2024

Keywords

• nonn

Comments

This sequence is different from A350894.

Crossrefs

Cf. A003106, A373073, A373074, A373076.

Cf. A350898, A373069.

Programs

PARI

my(N=80, x='x+O('x^N)); Vec(sum(k=0, N, x^(4*k^2+k)/prod(j=1, k, 1-x^j)))

Formula

G.f.: Sum_{k>=0} x^(4*k^2+k)/Product_{j=1..k} (1-x^j).