cp's OEIS Frontend

A118794 E.g.f.: 1 - exp((-1 + sqrt(5 - 4*exp(x)) )/2).

%I A118794 #15 Mar 04 2018 03:06:09
%S A118794 0,1,2,11,121,1902,38381,945989,27552260,925920081,35265751869,
%T A118794 1501219998148,70632987480771,3639861179067661,203881981765871618,
%U A118794 12333901891547136559,801418950244634922973,55665376886060309513990
%N A118794 E.g.f.: 1 - exp((-1 + sqrt(5 - 4*exp(x)) )/2).
%C A118794 Also equals the row sums of triangle A118793 (offset without leading zero).
%F A118794 a(n) = (n-1)!*Sum_{k=0..n-1} [x^k] (x/log(1-x-x^2))^n/(n-1-k)! for n>0.
%F A118794 a(n) = sum(m=1..n, ((-1)^(m+1)*sum(k=0..n-m, ((k+m-1)!*binomial(2*k+m-1,k+m-1)*stirling2(n,k+m))))/(m-1)!). - _Vladimir Kruchinin_, Jul 02 2011
%F A118794 a(n) ~ sqrt(5/2) * n^(n-1) / (2 * exp(n+1/2) * (log(5/4))^(n-1/2)). - _Vaclav Kotesovec_, Jul 31 2014
%e A118794 E.g.f.: A(x) = x + 2/2*x^2 + 11/6*x^3 + 121/24*x^4 + 1902/120*x^5 + ...
%t A118794 With[{nn=20},CoefficientList[Series[1-Exp[(Sqrt[5-4Exp[x]]-1)/2],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jun 07 2014 *)
%o A118794 (PARI) {a(n)=local(x=X+X^2*O(X^n));n!*polcoeff(1-exp((-1+sqrt(5-4*exp(x)))/2),n,X)}
%o A118794 for(n=0,30,print1(a(n),", "))
%o A118794 (PARI) /* As the row sums of A118793: */
%o A118794 {a(n)=local(x=X+X^2*O(X^n));if(n<1,0, -(n-1)!*sum(k=0,n-1,polcoeff(((x/log(1-x-x^2)))^n/(n-1-k)!,k,X)))}
%o A118794 for(n=0,30,print1(a(n),", "))
%o A118794 (Maxima)
%o A118794 a(n):=sum(((-1)^(m+1)*sum(((k+m-1)!*binomial(2*k+m-1,k+m-1)*stirling2(n,k+m)),k,0,n-m))/(m-1)!,m,1,n); /* _Vladimir Kruchinin_, Jul 02 2011 */
%Y A118794 Cf. A118793, A118795.
%K A118794 nonn
%O A118794 0,3
%A A118794 _Paul D. Hanna_, Apr 30 2006