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%I #2 Mar 30 2012 18:37:21
%S 1,3,28,575,21216,1242892,106459312,12577403841,1962856001440,
%T 391431498879806,97160350830990624,29387077319612739025,
%U 10642369538735639329912,4547196797035053394680280
%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=1: x + x^2 + x^3/2! + x^4/3! + x^5/4! + x^6/5! +...
%e n=2: (1)*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!+...
%e n=7: x + 7*x^2 +91*x^3/2! +1708*x^4/3! +41629*x^5/4! +(1242892)*x^6/5! +...
%e This sequence starts with the above coefficients in parenthesis.
%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, A174481, A174482, A174484.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Apr 09 2010
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