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%I #2 Mar 30 2012 18:37:16
%S 1,2,14,194,4280,134232,5587408,294882464,19102334112,1482726089600,
%T 135370060595264,14325189014356992,1736329123715436544,
%U 238698935851482530816,36911830664814417907200
%N E.g.f.: A(x) = exp( Sum_{n>=1} n*(n+3)/2 * a(n-1)*x^n/n! ) = Sum_{n>=0} a(n)*x^n/n! with a(0)=1.
%F a(n) = Sum_{k=1..n} k*(k+3)/2 * C(n-1,k-1)*a(k-1)*a(n-k) for n>0, with a(0)=1.
%e E.g.f: A(x) = 1 + 2*x + 14*x^2/2! + 194*x^3/3! + 4280*x^4/4! + 134232*x^5/5! +...
%e log(A(x)) = 2*1*x + 5*2*x^2/2! + 9*14*x^3/3! + 14*194*x^4/4! + 20*4280*x^5/5! +...
%o (PARI) {a(n)=if(n==0,1,n!*polcoeff(exp(sum(k=1,n,k*(k+3)/2*a(k-1)*x^k/k!)+x*O(x^n)),n))}
%o (PARI) {a(n)=if(n==0,1,sum(k=1,n,k*(k+3)/2*binomial(n-1,k-1)*a(k-1)*a(n-k)))}
%Y Cf. A156325, A156326.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Feb 08 2009
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