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

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

Offset: 0

Author

Paul D. Hanna, Dec 28 2007

Keywords

• nonn

Links

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

Crossrefs

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

Programs

Magma

[Binomial(3^n,n): n in [0..25]]; // Vincenzo Librandi, Sep 13 2016

Mathematica

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

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

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