A196794 a(n) = Sum_{k=0..n} binomial(n,k)*2^k*(k+1)^(n-k).
1, 3, 13, 69, 425, 2953, 22701, 190445, 1725777, 16757649, 173244629, 1896821941, 21897166137, 265525063001, 3371067773565, 44683137692157, 616811052816545, 8847765111928609, 131622808197394341, 2027097866771329349, 32267707989783480201, 530125689222591861993
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..523
Programs
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Maple
S:= series(exp(x+2*x*exp(x)),x,51): seq(coeff(S,x,j)*j!,j=0..50); # Robert Israel, Jan 20 2017
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PARI
{a(n)=sum(k=0,n,binomial(n,k)*2^k*(k+1)^(n-k))} -
PARI
{a(n)=polcoeff(sum(m=0,n,2^m*x^m/(1-(m+1)*x+x*O(x^n))^(m+1)),n)} -
PARI
{a(n)=n!*polcoeff(exp(x+2*x*exp(x+x*O(x^n))),n)}
Formula
O.g.f.: Sum_{n>=0} 2^n*x^n/(1 - (n+1)*x)^(n+1).
E.g.f.: exp(x + 2*x*exp(x)).