A373069 - OEIS

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A373069

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

4

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

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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