A196795 - OEIS

A196795

a(n) = Sum_{k=0..n} binomial(n,k)*3^k*(k+1)^(n-k).

1, 4, 22, 145, 1096, 9259, 85924, 865183, 9364864, 108173827, 1325589676, 17149360111, 233271228880, 3324545097475, 49493784653644, 767665750130839, 12376226335249024, 206967901014192643, 3583561993192959436, 64136093489935863583, 1184711492540805987856

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

FORMULA

O.g.f.: Sum_{n>=0} 3^n*x^n/(1 - (n+1)*x)^(n+1).

E.g.f.: exp(x + 3*x*exp(x)).

MATHEMATICA

Table[Sum[Binomial[n, k]3^k (k+1)^(n-k), {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Nov 12 2012 *)

PROG

(PARI) {a(n)=sum(k=0, n, binomial(n, k)*3^k*(k+1)^(n-k))}