A136393 a(n) = C(3^n,n).

1, 3, 36, 2925, 1663740, 6774333588, 204208594169580, 47025847059877940202, 84798009611754271531960140, 1219731290030242386267605060168700, 141916030352038369973126553950792759280336

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..45

Formula

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

a(n) = (1/n!) * Sum_{k=0..n} Stirling1(n, k) * 3^(n*k). - Paul D. Hanna, Feb 05 2023

a(n) ~ 3^(n^2)/n!. - Vaclav Kotesovec, Jul 02 2016

Mathematica

Table[Binomial[3^n, n], {n, 0, 10}] (* Vaclav Kotesovec, Jul 02 2016 *)

Prog

(PARI) a(n)=binomial(3^n, n)
(PARI) /* G.f. A(x) as Sum of Series: */
a(n)=polcoeff(sum(k=0, n, log(1+3^k*x +x*O(x^n))^k/k!), n)
(PARI) {a(n) = (1/n!) * sum(k=0, n, stirling(n, k, 1) * 3^(n*k) )}
for(n=0, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Feb 05 2023
(Magma) [Binomial(3^n, n): n in [0..25]]; // Vincenzo Librandi, Sep 13 2016

Crossrefs

Cf. A014070 (C(2^n, n)).

Sequence in context: A289315 A102579 A368076 * A168370 A325907 A158093

Adjacent sequences: A136390 A136391 A136392 * A136394 A136395 A136396

Keyword

nonn

Author

Paul D. Hanna, Dec 28 2007

Status

approved