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%I #2 Mar 30 2012 18:37:21
%S 1,1,6,102,3400,187455,15441636,1776667928,272145104736,
%T 53540399628405,13156413372354340,3949011172491569316,
%U 1421739781364268435576,604701975767931070422939,299969585267917154906689660
%N a(n) = coefficient of x^n/(n-1)! in the (n-1)-th iteration of x*exp(x) for n>=1.
%e The initial n-th iterations of x*exp(x) begin:
%e n=0: (1)*x;
%e n=1: x + (1)*x^2 + x^3/2! + x^4/3! + x^5/4! + x^6/5! +...
%e n=2: x + 2*x^2 +(6)*x^3/2! + 23*x^4/3! + 104*x^5/4! + 537*x^6/5! +...
%e n=3: x + 3*x^2 +15*x^3/2! +(102)*x^4/3! +861*x^5/4! +8598*x^6/5! +...
%e n=4: x + 4*x^2 +28*x^3/2! +274*x^4/3! +(3400)*x^5/4! +50734*x^6/5! +...
%e n=5: x + 5*x^2 +45*x^3/2! +575*x^4/3! +9425*x^5/4! +(187455)*x^6/5!+...
%e n=6: x + 6*x^2 +66*x^3/2! +1041*x^4/3! +21216*x^5/4!+527631*x^6/5! + (15441636)*x^7/6! +...
%e This sequence starts with the above coefficients in parathesis.
%o (PARI) {a(n)=local(E=x*exp(x+x*O(x^n)), F=x); for(i=1, n-1, F=subst(F, x, E)); (n-1)!*polcoeff(F, n)}
%Y Cf. A174480, A174482, A174483, A174484.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Apr 09 2010
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