cp's OEIS Frontend

A196794 a(n) = Sum_{k=0..n} binomial(n,k)*2^k*(k+1)^(n-k).

%I A196794 #13 Jan 20 2017 18:30:23
%S A196794 1,3,13,69,425,2953,22701,190445,1725777,16757649,173244629,
%T A196794 1896821941,21897166137,265525063001,3371067773565,44683137692157,
%U A196794 616811052816545,8847765111928609,131622808197394341,2027097866771329349,32267707989783480201,530125689222591861993
%N A196794 a(n) = Sum_{k=0..n} binomial(n,k)*2^k*(k+1)^(n-k).
%H A196794 Robert Israel, <a href="/A196794/b196794.txt">Table of n, a(n) for n = 0..523</a>
%F A196794 O.g.f.: Sum_{n>=0} 2^n*x^n/(1 - (n+1)*x)^(n+1).
%F A196794 E.g.f.: exp(x + 2*x*exp(x)).
%p A196794 S:= series(exp(x+2*x*exp(x)),x,51):
%p A196794 seq(coeff(S,x,j)*j!,j=0..50); # _Robert Israel_, Jan 20 2017
%o A196794 (PARI) {a(n)=sum(k=0,n,binomial(n,k)*2^k*(k+1)^(n-k))}
%o A196794 (PARI) {a(n)=polcoeff(sum(m=0,n,2^m*x^m/(1-(m+1)*x+x*O(x^n))^(m+1)),n)}
%o A196794 (PARI) {a(n)=n!*polcoeff(exp(x+2*x*exp(x+x*O(x^n))),n)}
%Y A196794 Cf. A080108, A196795.
%K A196794 nonn
%O A196794 0,2
%A A196794 _Paul D. Hanna_, Oct 06 2011