A373069 Number of partitions of n such that (smallest part) >= 4*(number of parts).

1, 0, 0, 0, 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, 13, 13, 15, 16, 18, 19, 22, 23, 26, 28, 31, 33, 37, 39, 43, 46, 50, 53, 58, 61, 66, 70, 75, 79, 85, 89, 95, 100, 107, 112, 120, 126, 135, 142, 152, 160, 172, 181, 194, 205, 220, 232, 249, 263

Offset

0,17

Links

Table of n, a(n) for n=0..79.

Formula

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

Crossrefs

Cf. A003114, A373067, A373068, A373070.

Cf. A350898, A373075.

Sequence in context: A330878 A373075 A350894 * A109728 A327036 A358854

Adjacent sequences: A373066 A373067 A373068 * A373070 A373071 A373072

Keyword

nonn

Author

Seiichi Manyama, May 22 2024

Status

approved