A179432 a(n) = C(2*3^(n-1), n).

1, 2, 15, 816, 316251, 873642672, 17743125256857, 2739097835911193328, 3301626910467952067341626, 31698997711344336177849363574320, 2460103385023594223069956382123378560008

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.

Links

Table of n, a(n) for n=0..10.

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

Cf. A179430, A179431, A136393, A179433, A179434.

Sequence in context: A038017 A012993 A216331 * A007542 A090604 A007467

Adjacent sequences: A179429 A179430 A179431 * A179433 A179434 A179435

Keyword

nonn

Author

Paul D. Hanna, Jul 20 2010

Status

approved