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A179432 a(n) = C(2*3^(n-1), n). 4

%I

%S 1,2,15,816,316251,873642672,17743125256857,2739097835911193328,

%T 3301626910467952067341626,31698997711344336177849363574320,

%U 2460103385023594223069956382123378560008

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

%C 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.

%F G.f.: A(x) = Sum_{n>=0} (2/3)^n * log(1 + 3^n*x)^n / n!.

%F a(n) ~ 2^n * 3^(n*(n-1)) / n!. - _Vaclav Kotesovec_, Jul 02 2016

%e G.f.: A(x) = 1 + 2*x + 15*x^2 + 816*x^3 + 316251*x^4 +...

%e 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!) +...

%t Table[Binomial[2*3^(n-1),n], {n,0,15}] (* _Vaclav Kotesovec_, Jul 02 2016 *)

%o (PARI) {a(n)=binomial(2*3^(n-1), n)}

%o (PARI) /* G.f. A(x) as Sum of Series: */

%o {a(n)=polcoeff(sum(k=0, n, (2/3)^k*log(1+3^k*x +x*O(x^n))^k/k!), n)}

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

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 20 2010

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Last modified June 24 10:00 EDT 2019. Contains 324323 sequences. (Running on oeis4.)