A347869 Number of partitions of n such that 5*(greatest part) >= (number of parts).

1, 2, 3, 5, 7, 10, 14, 21, 29, 41, 55, 75, 98, 131, 171, 225, 290, 376, 479, 613, 775, 981, 1231, 1545, 1923, 2393, 2959, 3656, 4492, 5515, 6737, 8223, 9994, 12133, 14676, 17732, 21351, 25679, 30793, 36879, 44049, 52549, 62535, 74329, 88153, 104418, 123437, 145746, 171765, 202193

Offset: 1

Author

Seiichi Manyama, Jan 25 2022

Keywords

• nonn

Comments

Also, the number of partitions of n such that (greatest part) <= 5*(number of parts).

Crossrefs

Cf. A064174, A237755, A347867, A347868.

Cf. A348164.

Programs

PARI

my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k*prod(j=1, k, (1-x^(5*k+j-1))/(1-x^j))))

Formula

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