A046785 Number of partitions of n with equal nonzero number of parts congruent to each of 0, 1, 3 and 4 (mod 5).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 4, 1, 5, 1, 5, 11, 5, 16, 6, 17, 26, 17, 41, 21, 46, 57, 47, 92, 61, 108, 122, 114, 193, 151, 233, 254, 253, 385, 344, 472, 520, 527, 750, 724, 922, 1035, 1054, 1426, 1458, 1746, 2015, 2035, 2676, 2811, 3248, 3818

Offset

0,19

Links

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

Formula

G.f.: (Sum_{k>0} x^(13*k)/(Product_{j=1..k} 1 - x^(5*j))^3)/(Product_{j>=0} 1 - x^(5*j+2)). - Andrew Howroyd, Sep 16 2019

Prog

(PARI) seq(n)={Vec(sum(k=1, n\13, x^(13*k)/prod(j=1, k, 1 - x^(5*j) + O(x*x^(n-13*k)))^4)/prod(j=0, n\5, 1 - x^(5*j+2) + O(x*x^n)), -(n+1))} \\ Andrew Howroyd, Sep 16 2019

Crossrefs

Cf. A046787.

Sequence in context: A195986 A348492 A353576 * A060044 A323413 A019303

Adjacent sequences: A046782 A046783 A046784 * A046786 A046787 A046788

Keyword

nonn

Author

David W. Wilson

Status

approved