OFFSET
0,2
COMMENTS
a(n) is Euler transform of A010854. - Alois P. Heinz, Oct 17 2008
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Transforms
FORMULA
a(0) = 1, a(n) = (15/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017
a(n) ~ m^((m+1)/4) * exp(Pi*sqrt(2*m*n/3)) / (2^((3*m+5)/4) * 3^((m+1)/4) * n^((m+3)/4)) * (1 - ((9+Pi^2)*m^2+36*m+27) / (24*Pi*sqrt(6*m*n))), set m = 15. - Vaclav Kotesovec, Jun 28 2025
Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = 32 * exp(-5*Pi/8) * 2^(5/8) * Gamma(3/4)^15 / Pi^(15/4) = A388362. - Simon Plouffe, Sep 15 2025
MAPLE
with(numtheory): a:= proc(n) option remember; `if`(n=0, 1, add(add(d*15, d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..40); # Alois P. Heinz, Oct 17 2008
MATHEMATICA
CoefficientList[Series[1/QPochhammer[x]^15, {x, 0, 30}], x] (* Indranil Ghosh, Mar 27 2017 *)
PROG
(PARI) Vec(1/eta(x)^15 + O(x^30)) \\ Indranil Ghosh, Mar 27 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved