A373068 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A373068

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

4

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

(list; graph; refs; listen; history; text; internal format)

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