cp's OEIS Frontend

A135744 E.g.f.: A(x) = Sum_{n>=0} exp( n*(n+1)*x ) * x^n/n!.

%I A135744 #9 Nov 05 2016 14:17:13
%S A135744 1,1,5,31,297,3781,60373,1188699,28003825,772499593,24613769061,
%T A135744 894386029879,36653691106585,1679283513161229,85360981759418485,
%U A135744 4781873479864452211,293487961919565420897,19633825959679051986961
%N A135744 E.g.f.: A(x) = Sum_{n>=0} exp( n*(n+1)*x ) * x^n/n!.
%H A135744 G. C. Greubel, <a href="/A135744/b135744.txt">Table of n, a(n) for n = 0..250</a>
%F A135744 a(n) = Sum_{k=0..n} C(n,k) * ( k*(k+1) )^(n-k).
%F A135744 O.g.f.: Sum_{n>=0} x^n / (1 - n*(n+1)*x)^(n+1). - _Paul D. Hanna_, Jul 30 2014
%t A135744 Flatten[{1, Table[Sum[Binomial[n, k]*(2*Binomial[k + 1, 2])^(n - k), {k, 0, n}], {n, 1, 25}]}] (* _G. C. Greubel_, Nov 05 2016 *)
%o A135744 (PARI) {a(n)=sum(k=0,n,binomial(n,k)*(k*(k+1))^(n-k))}
%o A135744 for(n=0,25,print1(a(n),", "))
%o A135744 (PARI) {a(n)=n!*polcoeff(sum(k=0,n,exp(k*(k+1)*x +x*O(x^n))*x^k/k!),n)}
%o A135744 for(n=0,25,print1(a(n),", "))
%o A135744 (PARI) /* From Sum_{n>=0} x^n/(1 - n*(n+1)*x)^(n+1): */
%o A135744 {a(n)=polcoeff(sum(k=0, n, x^k/(1-k*(k+1)*x +x*O(x^n))^(k+1)), n)}
%o A135744 for(n=0,25,print1(a(n),", "))
%Y A135744 Cf. variants: A135742, A135743, A135745, A135746, A135747.
%K A135744 nonn
%O A135744 0,3
%A A135744 _Paul D. Hanna_, Nov 27 2007