OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
W. Y. C. Chen, K. Q. Ji, H.-T. Jin and E. Y. Y. Shen, On the number of partitions with designated summands, J. Number Theory, 133 (2013), 2929-2938.
FORMULA
a(n) = (1/3) * A077285(3*n+2).
a(n) ~ 5^(3/4) * exp(sqrt(10*n/3)*Pi) / (2^(11/4) * 3^(15/4) * n^(5/4)). - Vaclav Kotesovec, Oct 09 2017
MATHEMATICA
nmax = 40; CoefficientList[Series[Product[((1 - x^(3*k))^3 * (1 - x^(6*k))^3) / ((1 - x^k)^5 * (1 - x^(2*k))^3), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 09 2017 *)
max = 30; QP = QPochhammer; s = QP[q^6]/(QP[q]*QP[q^2]*QP[q^3]) + O[q]^(3 max + 3); (1/3)*Table[CoefficientList[s, q][[3*n + 3]], {n, 0, max}] (* Jean-François Alcover, Oct 10 2017, from 1st formula *)
PROG
(PARI) m = 40; Vec(prod(k=1, m, ((1 - q^(3*k))^3*(1 - q^(6*k))^3)/((1 - q^k)^5*(1 - q^(2*k))^3)) + O(q^m)) \\ Michel Marcus, Oct 10 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 09 2017
STATUS
approved