OFFSET
0,2
FORMULA
G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A363311.
a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(3*n+2*k-2,n-1) for n > 0.
a(n) ~ c*(-1)^(n+1)*27^n*4^(-n)*3F2([-n, 3*n/2, (3n-1)/2], [n, n+1/2], -1)*n^(-3/2), with c = 1/(3*sqrt(3*Pi)). - Stefano Spezia, Oct 21 2023
PROG
(PARI) a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(3*n+2*k-2, n-1))/n);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 22 2023
STATUS
approved