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%I #2 Mar 30 2012 18:37:16
%S 1,1,4,26,292,3468,69664,1208936,32822456,858979216,28933584112,
%T 836115182512,40673697842208,1381857061152896,67261437417875776,
%U 3297904559465926208,192628214559932492928,8815748379077085483264
%N E.g.f.: A(x) = exp( Sum_{n>=1} sigma(n) * 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} sigma(k) * 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 + x + 4*x^2/2! + 26*x^3/3! + 292*x^4/4! + 3468*x^5/5! +...
%e log(A(x)) = x + 3*1*x^2/2! + 4*4*x^3/3! + 7*26*x^4/4! + 6*292*x^5/5! + 12*3468*x^6/6! +...
%o (PARI) {a(n)=if(n==0,1,n!*polcoeff(exp(sum(k=1,n,sigma(k)*a(k-1)*x^k/k!)+x*O(x^n)),n))}
%o (PARI) {a(n)=if(n==0,1,sum(k=1,n,sigma(k)*binomial(n-1,k-1)*a(k-1)*a(n-k)))}
%Y Cf. A000203 (sigma).
%K nonn
%O 0,3
%A _Paul D. Hanna_, Feb 08 2009
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