A046786 Number of partitions of n with equal nonzero number of parts congruent to each of 0, 2, 3 and 4 (mod 5).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 5, 6, 6, 6, 6, 16, 21, 22, 22, 23, 43, 58, 63, 64, 68, 104, 139, 155, 160, 175, 236, 307, 347, 364, 405, 509, 640, 727, 772, 874, 1054, 1285, 1456, 1562, 1784, 2106, 2501, 2819, 3046, 3502, 4084, 4756, 5322, 5782

Offset

0,20

Links

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

Formula

G.f.: (Sum_{k>0} x^(14*k)/(Product_{j=1..k} 1 - x^(5*j))^3)/(Product_{j>=0} 1 - x^(5*j+1)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=1, n\14, x^(14*k)/prod(j=1, k, 1 - x^(5*j) + O(x*x^(n-14*k)))^4)/prod(j=0, n\5, 1 - x^(5*j+1) + O(x*x^n)), -(n+1))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046787.

Sequence in context: A074826 A018246 A101101 * A035591 A256683 A120206

Adjacent sequences: A046783 A046784 A046785 * A046787 A046788 A046789

Keyword

nonn

Author

David W. Wilson

Status

approved