A107234 Expansion of 1 / Product_{n>=0} (1-q^(5n+1))(1-q^(5n+2))(1-q^(5n+3)).

1, 1, 2, 3, 4, 5, 8, 10, 14, 18, 23, 29, 38, 47, 60, 74, 92, 112, 139, 168, 205, 247, 298, 356, 429, 509, 607, 718, 850, 1000, 1180, 1381, 1620, 1890, 2206, 2564, 2983, 3453, 4000, 4618, 5330, 6133, 7059, 8097, 9289, 10630, 12159, 13877

Offset

0,3

Comments

a(n) is the number of partitions of n into parts 5k+1, 5k+2 or 5k+3. - George Beck, Aug 09 2020

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ Pi^(1/5) * exp(Pi*sqrt(2*n/5)) / (Gamma(4/5) * 2^(3/5) * 5^(9/10) * n^(3/5)). - Vaclav Kotesovec, Jan 07 2021

Mathematica

nmax = 50; CoefficientList[Series[1/Product[(1 - x^(5*k+1))*(1 - x^(5*k+2))*(1 - x^(5*k+3)), {k, 0, nmax/5}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 07 2021 *)

Crossrefs

Cf. A035959, A107235, A107236, A107237.

Sequence in context: A058664 A238479 A035562 * A035943 A240177 A035555

Adjacent sequences: A107231 A107232 A107233 * A107235 A107236 A107237

Keyword

nonn

Author

Ralf Stephan, May 13 2005

Status

approved