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 A179432 a(n) = C(2*3^(n-1), n). 4
 1, 2, 15, 816, 316251, 873642672, 17743125256857, 2739097835911193328, 3301626910467952067341626, 31698997711344336177849363574320, 2460103385023594223069956382123378560008 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified May 19 07:05 EDT 2019. Contains 323386 sequences. (Running on oeis4.)