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%I #9 Nov 05 2016 15:03:55
%S 1,0,2,9,88,985,14976,278929,6208000,163268865,4979147680,
%T 173500986241,6838921208736,302161792811905,14840867887070512,
%U 804732692174218305,47888731015720316416,3110871265807567331329,219546952410733092279360
%N E.g.f.: A(x) = Sum_{n>=0} exp( (n^2-1)*x ) * x^n/n!.
%C n divides a(n) for n>=1.
%H G. C. Greubel, <a href="/A135747/b135747.txt">Table of n, a(n) for n = 0..250</a>
%F a(n) = Sum_{k=0..n} C(n,k) * (k^2-1)^(n-k).
%F O.g.f.: Sum_{n>=0} x^n / (1 - (n^2-1)*x)^(n+1). - _Paul D. Hanna_, Jul 30 2014
%t Flatten[{1, Table[Sum[Binomial[n, k]*(k^2 - 1)^(n - k), {k, 0, n}], {n,1,25}]}] (* _G. C. Greubel_, Nov 05 2016 *)
%o (PARI) {a(n)=sum(k=0,n,binomial(n,k)*(k^2-1)^(n-k))}
%o for(n=0,25,print1(a(n),", "))
%o (PARI) {a(n)=n!*polcoeff(sum(k=0,n,exp((k^2-1)*x +x*O(x^n))*x^k/k!),n)}
%o for(n=0,25,print1(a(n),", "))
%o (PARI) /* From Sum_{n>=0} x^n/(1 - (n^2-1)*x)^(n+1): */
%o {a(n)=polcoeff(sum(k=0, n, x^k/(1-(k^2-1)*x +x*O(x^n))^(k+1)), n)}
%o for(n=0,25,print1(a(n),", "))
%Y Cf. variants: A135742, A135743, A135744, A135745, A135746.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Nov 27 2007
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