OFFSET
0,2
COMMENTS
Equals column 0 in the matrix square of triangle T=A179430 where column 0 of T^m equals C(m*3^(n-1), n) at row n for n>=0, m>=0.
FORMULA
G.f.: A(x) = Sum_{n>=0} (2/3)^n * log(1 + 3^n*x)^n / n!.
a(n) ~ 2^n * 3^(n*(n-1)) / n!. - Vaclav Kotesovec, Jul 02 2016
EXAMPLE
G.f.: A(x) = 1 + 2*x + 15*x^2 + 816*x^3 + 316251*x^4 +...
A(x) = 1 + 2*log(1+3*x)/3 + 2^2*log(1+3^2*x)^2/(3^2*2!) + 2^3*log(1+3^3*x)^3/(3^3*3!) + 2^4*log(1+3^4*x)^4/(3^4*4!) +...
MATHEMATICA
Table[Binomial[2*3^(n-1), n], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *)
PROG
(PARI) {a(n)=binomial(2*3^(n-1), n)}
(PARI) /* G.f. A(x) as Sum of Series: */
{a(n)=polcoeff(sum(k=0, n, (2/3)^k*log(1+3^k*x +x*O(x^n))^k/k!), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 20 2010
STATUS
approved