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%I #2 Mar 30 2012 18:37:21
%S 1,3,15,102,861,8598,98547,1270160,18138601,283754826,4818884319,
%T 88186786020,1728395865021,36091833338174,799408841413051,
%U 18708996086926272,461095012437724881,11931573394008790290
%N a(n) = coefficient of x^n/(n-1)! in the 3-fold iteration of x*exp(x).
%F a(n) = Sum_{k=0..n, j=0..n-k} C(n,k)*C(n-k,j)*(k+1)^j*(k+1+j)^(n-k-j).
%F O.g.f.: Sum_{n>=1} A080108(n)*x^n/(1-n*x)^n, where A080108(n) = [x^n/(n-1)! ] E(E(x)) and E(x) = x*exp(x).
%e E.g.f.: x + 3*x^2 + 15*x^3/2! + 102*x^4/3! + 861*x^5/4! +...
%o (PARI) {a(n)=local(F=x, xEx=x*exp(x+x*O(x^n)));for(i=1,3,F=subst(F, x, xEx));(n-1)!*polcoeff(F, n)}
%o (PARI) {a(n)=sum(k=0,n-1,binomial(n-1,k)*sum(j=0,n-1-k,binomial(n-1-k,j)*(k+1)^j*(k+1+j)^(n-1-k-j)))}
%Y Cf. A174480, A080108, A174494, A174495, A174496.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Apr 17 2010
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