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 A174495 a(n) = coefficient of x^n/(n-1)! in the 5-fold iteration of x*exp(x). 4

%I

%S 1,5,45,575,9425,187455,4367245,116322645,3479863345,115353325835,

%T 4192244804645,165607074622665,7060695856372105,322973775761169135,

%U 15770136907303728205,818373668098974428885,44963322539225628107105

%N a(n) = coefficient of x^n/(n-1)! in the 5-fold iteration of x*exp(x).

%F O.g.f.: Sum_{n>=1} A174494(n)*x^n/(1-n*x)^n, where A174494(n) = [x^n/(n-1)! ] E(E(E(E(x)))) and E(x) = x*exp(x).

%e E.g.f.: x + 5*x^2 + 45*x^3/2! + 575*x^4/3! + 9425*x^5/4! +...

%o (PARI) {a(n)=local(F=x, xEx=x*exp(x+x*O(x^n))); for(i=1,5,F=subst(F, x, xEx));(n-1)!*polcoeff(F, n)}

%Y Cf. A174480, A080108, A174493, A174494, A174496.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Apr 17 2010

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Last modified March 31 20:29 EDT 2023. Contains 361672 sequences. (Running on oeis4.)