A373067 Number of partitions of n such that (smallest part) >= 2*(number of parts).

1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 8, 8, 10, 11, 13, 14, 17, 18, 21, 23, 26, 28, 32, 34, 39, 42, 47, 51, 58, 62, 70, 76, 85, 92, 103, 111, 124, 134, 148, 160, 177, 190, 210, 226, 248, 267, 293, 315, 345, 371, 405, 436, 476, 511, 557, 599, 651, 700, 760, 816

Offset

0,9

Links

Table of n, a(n) for n=0..67.

Formula

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

Prog

(PARI) my(N=70, x='x+O('x^N)); Vec(sum(k=0, N, x^(2*k^2)/prod(j=1, k, 1-x^j)))

Crossrefs

Cf. A003114, A373068, A373069, A373070.

Cf. A069910, A350893, A373073.

Sequence in context: A026829 A025154 A241827 * A096401 A264593 A026828

Adjacent sequences: A373064 A373065 A373066 * A373068 A373069 A373070

Keyword

nonn

Author

Seiichi Manyama, May 22 2024

Status

approved