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%I #16 Feb 06 2023 10:05:55
%S 1,3,36,2925,1663740,6774333588,204208594169580,47025847059877940202,
%T 84798009611754271531960140,1219731290030242386267605060168700,
%U 141916030352038369973126553950792759280336
%N a(n) = C(3^n,n).
%H Vincenzo Librandi, <a href="/A136393/b136393.txt">Table of n, a(n) for n = 0..45</a>
%F G.f.: A(x) = Sum_{n>=0} log(1 + 3^n*x)^n / n!.
%F a(n) = (1/n!) * Sum_{k=0..n} Stirling1(n, k) * 3^(n*k). - _Paul D. Hanna_, Feb 05 2023
%F a(n) ~ 3^(n^2)/n!. - _Vaclav Kotesovec_, Jul 02 2016
%t Table[Binomial[3^n,n], {n,0,10}] (* _Vaclav Kotesovec_, Jul 02 2016 *)
%o (PARI) a(n)=binomial(3^n,n)
%o (PARI) /* G.f. A(x) as Sum of Series: */
%o a(n)=polcoeff(sum(k=0,n,log(1+3^k*x +x*O(x^n))^k/k!),n)
%o (PARI) {a(n) = (1/n!) * sum(k=0, n, stirling(n, k, 1) * 3^(n*k) )}
%o for(n=0, 20, print1(a(n), ", ")) \\ _Paul D. Hanna_, Feb 05 2023
%o (Magma) [Binomial(3^n,n): n in [0..25]]; // _Vincenzo Librandi_, Sep 13 2016
%Y Cf. A014070 (C(2^n, n)).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Dec 28 2007
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