OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 8.
FORMULA
a(n) ~ (5/3)^(1/4) * exp(Pi * sqrt(5*n/3)) / (16 * n^(3/4)). - Vaclav Kotesovec, Mar 05 2015
a(0) = 1, a(n) = (5/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017
G.f.: exp(5*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018
MATHEMATICA
nmax=50; CoefficientList[Series[Product[(1+q^m)^5, {m, 1, nmax}], {q, 0, nmax}], q] (* Vaclav Kotesovec, Mar 05 2015 *)
PROG
(PARI) x='x+O('x^51); Vec(prod(m=1, 50, (1 + x^m)^5)) \\ Indranil Ghosh, Apr 03 2017
(Magma) Coefficients(&*[(1+x^m)^5:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved