A179431 a(n) = binomial(3^(n-1), n).

1, 1, 3, 84, 17550, 25621596, 268715232324, 21091830512086620, 12814543323816738705045, 61742372998425082372103866380, 2399699340005498870742886195375900380, 761689137813999393167583510790986701377432464, 1992997938492157367948224731863936229108552184201415196

Offset: 0

Author

Paul D. Hanna, Jul 20 2010

Keywords

• nonn

Comments

Equals column 0 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.

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 84*x^3 + 17550*x^4 + 25621596*x^5 +...
A(x) = 1 + log(1+3*x)/3 + log(1+3^2*x)^2/(3^2*2!) + log(1+3^3*x)^3/(3^3*3!) + log(1+3^4*x)^4/(3^4*4!) +...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..40

Crossrefs

Cf. A179430, A179432, A136393, A179433, A179434.

Programs

Mathematica

Table[Binomial[3^(n-1),n], {n,0,15}] (* Vaclav Kotesovec, Jul 02 2016 *)

PARI

a(n)=binomial(3^(n-1), n)

PARI

/* G.f. A(x) as Sum of Series: */
{a(n)=polcoeff(sum(k=0, n, (1/3)^k*log(1+3^k*x +x*O(x^n))^k/k!), n)}

Formula

G.f.: A(x) = Sum_{n>=0} (1/3)^n * log(1 + 3^n*x)^n / n!.

a(n) ~ 3^(n*(n-1)) / n!. - Vaclav Kotesovec, Jul 02 2016

Extensions

Terms a(11) and beyond from Andrew Howroyd, Apr 13 2021