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
Offset: 0
Keywords
Programs
-
Mathematica
Table[Sum[Binomial[n,k]3^k (k+1)^(n-k),{k,0,n}],{n,0,20}] (* Harvey P. Dale, Nov 12 2012 *) -
PARI
{a(n)=sum(k=0,n,binomial(n,k)*3^k*(k+1)^(n-k))} -
PARI
{a(n)=polcoeff(sum(m=0,n,3^m*x^m/(1-(m+1)*x+x*O(x^n))^(m+1)),n)} -
PARI
{a(n)=n!*polcoeff(exp(x+3*x*exp(x+x*O(x^n))),n)}
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)).