OFFSET
0,2
FORMULA
a(n) = [x^n] 1/sqrt(1 - 4*x*(1+x)^n).
log(a(n)) ~ n*(log(n) + (2*log(2) - 1)/log(n) - (1 - 1/log(n))*log(log(n) - 1)). - Vaclav Kotesovec, Mar 26 2023
MATHEMATICA
Table[Sum[Binomial[2*k, k]*Binomial[n*k, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 26 2023 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(2*k, k)*binomial(n*k, n-k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 26 2023
STATUS
approved