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

1,2

Comments

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

Links

Table of n, a(n) for n=1..50.

Formula

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

Prog

(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))))

Crossrefs

Cf. A064174, A237755, A347867, A347868.

Cf. A348164.

Sequence in context: A005688 A241550 A319564 * A221943 A120446 A082531

Adjacent sequences: A347866 A347867 A347868 * A347870 A347871 A347872

Keyword

nonn

Author

Seiichi Manyama, Jan 25 2022

Status

approved