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A179431 a(n) = C(3^(n-1), n). 4
1, 1, 3, 84, 17550, 25621596, 268715232324, 21091830512086620, 12814543323816738705045, 61742372998425082372103866380, 2399699340005498870742886195375900380 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

LINKS

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

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

EXAMPLE

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!) +...

MATHEMATICA

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

PROG

(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)}

CROSSREFS

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

Sequence in context: A086264 A160878 A152791 * A116303 A215911 A203510

Adjacent sequences:  A179428 A179429 A179430 * A179432 A179433 A179434

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 20 2010

STATUS

approved

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Last modified June 24 13:17 EDT 2019. Contains 324325 sequences. (Running on oeis4.)