A373068 Number of partitions of n such that (smallest part) >= 3*(number of parts).

1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 11, 12, 14, 15, 17, 19, 21, 23, 26, 28, 31, 34, 37, 40, 44, 47, 51, 55, 59, 63, 69, 73, 79, 85, 92, 98, 107, 114, 124, 133, 144, 154, 168, 179, 194, 208, 225, 240, 260, 277, 299, 319, 343, 365, 393, 417, 447, 476

Offset

0,13

Links

Table of n, a(n) for n=0..75.

Formula

G.f.: Sum_{k>=0} x^(3*k^2)/Product_{j=1..k} (1-x^j).

Prog

(PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k^2)/prod(j=1, k, 1-x^j)))

Crossrefs

Cf. A003114, A373067, A373069, A373070.

Cf. A350894, A373074.

Sequence in context: A373074 A248180 A025161 * A350893 A021895 A025160

Adjacent sequences: A373065 A373066 A373067 * A373069 A373070 A373071

Keyword

nonn

Author

Seiichi Manyama, May 22 2024

Status

approved