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%I #14 Dec 03 2015 19:11:11
%S 1,2,15,256,7935,392526,28498246,2863702080,381411964485,
%T 65129544696250,13888321460879976,3620285828450155008,
%U 1133432920326577483795,419923892646668363653350,181795302703808044653240000,90971411268941227901619966976
%N E.g.f.: x = Sum_{n>=1} a(n)*x^n/n! * exp(-n*(n+1)/2*x).
%C Compare e.g.f. to: x = Sum_{n>=1} n^(n-1)*x^n/n! * exp(-n*x), which generates coefficients for the series reversion of x*exp(-x).
%H Alois P. Heinz, <a href="/A195737/b195737.txt">Table of n, a(n) for n = 1..200</a>
%F G.f.: x = Sum_{n>=1} a(n)*x^n/(n*(1 + n*(n+1)/2*x)^n).
%e x = x*exp(-x) + 2*x^2/2!*exp(-3*x) + 15*x^3/3!*exp(-6*x) + 256*x^4/4!*exp(-10*x) + 7935*x^5/5!*exp(-15*x) +...+ a(n)*x^n/n!*exp(-n*(n+1)/2*x) +...
%e The coefficients a(n) also satisfy:
%e x = x/(1+x) + 2*x^2/(2*(1+3*x)^2) + 15*x^3/(3*(1+6*x)^3) + 256*x^4/(4*(1+10*x)^4) + 7935*x^5/(5*(1+15*x)^5) +...+ a(n)*x^n/(n*(1+n*(n+1)/2*x)^n) +...
%o (PARI) {a(n)=if(n<1,0,n!*polcoeff(x-sum(m=1,n-1,a(m)*x^m/m!*exp(-m*(m+1)/2*x+x*O(x^n))),n))}
%o (PARI) {a(n)=if(n<1,0,n*polcoeff(x-sum(m=1,n-1,a(m)*x^m/(m*(1+m*(m+1)/2*x+x*O(x^n))^m)),n))}
%Y Cf. A195736, A196304.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Sep 30 2011
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