A046771 Number of partitions of n with equal number of parts congruent to each of 0, 1, 2 and 3 (mod 5).

1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 5, 1, 2, 2, 6, 11, 3, 3, 7, 16, 23, 8, 9, 18, 38, 44, 24, 21, 44, 79, 86, 59, 52, 96, 157, 163, 141, 118, 199, 295, 318, 304, 259, 387, 549, 613, 632, 534, 736, 1006, 1179, 1240, 1070, 1364, 1842, 2217, 2366, 2074, 2508

Offset

0,17

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Formula

G.f.: (Sum_{k>=0} x^(11*k)/(Product_{j=1..k} 1 - x^(5*j))^3)/(Product_{j>=0} 1 - x^(5*j+4)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=0, n\11, x^(11*k)/prod(j=1, k, 1 - x^(5*j) + O(x*x^n))^4)/prod(j=0, n\5, 1 - x^(5*j+4) + O(x*x^n)))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046765.

Sequence in context: A140987 A097562 A275889 * A029762 A222214 A055185

Adjacent sequences: A046768 A046769 A046770 * A046772 A046773 A046774

Keyword

nonn

Author

David W. Wilson

Status

approved