A035370 Number of partitions of n into parts 5k or 5k+4.

0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 1, 2, 4, 3, 1, 2, 5, 7, 6, 2, 5, 9, 13, 9, 5, 10, 18, 21, 16, 10, 20, 30, 35, 25, 21, 35, 52, 55, 43, 37, 62, 83, 88, 68, 67, 102, 135, 135, 111, 112, 168, 208, 209, 173, 188, 265, 323, 314, 275, 300, 415, 485, 475, 421, 477, 632, 730, 703

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Programs

Mathematica

nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(5k+5))*(1 - x^(5k+4))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 27 2015 *)

Formula

a(n) ~ exp(2*Pi*sqrt(n/15)) * 5^(3/20) * Gamma(4/5) / (4 * 3^(13/20) * Pi^(1/5) * n^(23/20)). - Vaclav Kotesovec, Aug 27 2015