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A196794
a(n) = Sum_{k=0..n} binomial(n,k)*2^k*(k+1)^(n-k).
2
1, 3, 13, 69, 425, 2953, 22701, 190445, 1725777, 16757649, 173244629, 1896821941, 21897166137, 265525063001, 3371067773565, 44683137692157, 616811052816545, 8847765111928609, 131622808197394341, 2027097866771329349, 32267707989783480201, 530125689222591861993
OFFSET
0,2
LINKS
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)).
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
PROG
(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)}
CROSSREFS
Sequence in context: A067145 A192739 A088368 * A184818 A352370 A007808
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 06 2011
STATUS
approved