OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..300
FORMULA
a(n) = S2(3*n,2*n), where S2(n,k) is Stirling numbers of the second kind.
a(n) = (1/(2*n)!) * Sum_{k=0..2*n} (-1)^k * k^(3*n) * binomial(2*n,k).
a(n) ~ 3^(3*n) * n^(n - 1/2) / (sqrt(Pi*(1-c)) * 2^(n+1) * exp(n) * (3 - 2*c)^n * c^(2*n)), where c = -LambertW(-3*exp(-3/2)/2) = 0.62578253420128292093838... - Vaclav Kotesovec, Oct 02 2021
PROG
(PARI) a(n) = polcoef(1/prod(k=1, 2*n, 1-k*x+x*O(x^n)), n);
(PARI) a(n) = stirling(3*n, 2*n, 2);
(PARI) a(n) = sum(k=0, 2*n, (-1)^k*k^(3*n)*binomial(2*n, k))/(2*n)!;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 28 2021
STATUS
approved