cp's OEIS Frontend

A135745 E.g.f.: A(x) = Sum_{n>=0} exp((n-1)*x)^n * x^n/n!.

%I A135745 #9 Nov 05 2016 14:17:08
%S A135745 1,1,1,7,49,501,6841,115123,2362305,57768553,1646192881,53952383871,
%T A135745 2010872281969,84330050952733,3945169959883881,204416253047774251,
%U A135745 11655594262050124801,727189793270478477777,49395902623624761264865
%N A135745 E.g.f.: A(x) = Sum_{n>=0} exp((n-1)*x)^n * x^n/n!.
%H A135745 G. C. Greubel, <a href="/A135745/b135745.txt">Table of n, a(n) for n = 0..250</a>
%F A135745 a(n) = Sum_{k=0..n} C(n,k)*[k*(k-1)]^(n-k).
%F A135745 O.g.f.: Sum_{n>=0} x^n/(1 - n*(n-1)*x)^(n+1). - _Paul D. Hanna_, Jul 30 2014
%t A135745 Flatten[{1, Table[Sum[Binomial[n, k]*(k*(k - 1))^(n - k), {k, 0, n}], {n, 1, 25}]}] (* _G. C. Greubel_, Nov 05 2016 *)
%o A135745 (PARI) {a(n)=sum(k=0,n,binomial(n,k)*(k*(k-1))^(n-k))}
%o A135745 for(n=0,25,print1(a(n),", "))
%o A135745 (PARI) {a(n)=n!*polcoeff(sum(k=0,n,exp(k*(k-1)*x +x*O(x^n))*x^k/k!),n)}
%o A135745 for(n=0,25,print1(a(n),", "))
%o A135745 (PARI) /* From Sum_{n>=0} x^n/(1 - n*(n-1)*x)^(n+1): */
%o A135745 {a(n)=polcoeff(sum(k=0, n, x^k/(1-k*(k-1)*x +x*O(x^n))^(k+1)), n)}
%o A135745 for(n=0,25,print1(a(n),", "))
%Y A135745 Cf. variants: A135742, A135743, A135744, A135746, A135747.
%K A135745 nonn
%O A135745 0,4
%A A135745 _Paul D. Hanna_, Nov 27 2007