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

1, 5, 45, 575, 9425, 187455, 4367245, 116322645, 3479863345, 115353325835, 4192244804645, 165607074622665, 7060695856372105, 322973775761169135, 15770136907303728205, 818373668098974428885, 44963322539225628107105

Offset

1,2

Links

Table of n, a(n) for n=1..17.

Formula

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).

Example

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

Prog

(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)}

Crossrefs

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

Sequence in context: A062023 A169714 A084095 * A121414 A243678 A097328

Adjacent sequences: A174492 A174493 A174494 * A174496 A174497 A174498

Keyword

nonn

Author

Paul D. Hanna, Apr 17 2010

Status

approved