A136393 - OEIS

%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