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A174496 a(n) = coefficient of x^n/(n-1)! in the 6-fold iteration of x*exp(x). 3
1, 6, 66, 1041, 21216, 527631, 15441636, 518651881, 19630068656, 825581830491, 38159948599956, 1921319136589221, 104603652465885096, 6120324106269585751, 382829011514506048556, 25484466375276284094561 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..16.

FORMULA

O.g.f.: Sum_{n>=1} A174495(n)*x^n/(1-n*x)^n, where A174495(n) = [x^n/(n-1)! ] E(E(E(E(E(x))))) and E(x) = x*exp(x).

E.g.f. equals the 2-fold iteration of the e.g.f. of A174493.

E.g.f. equals the 3-fold iteration of the e.g.f. of A080108.

EXAMPLE

E.g.f.: x + 6*x^2 + 66*x^3/2! + 1041*x^4/3! + 21216*x^5/4! +...

PROG

(PARI) {a(n)=local(F=x, xEx=x*exp(x+x*O(x^n))); for(i=1, 6, F=subst(F, x, xEx)); (n-1)!*polcoeff(F, n)}

CROSSREFS

Cf. A174480, A080108, A174493, A174494, A174495.

Sequence in context: A360976 A360236 A128319 * A008548 A090358 A359462

Adjacent sequences: A174493 A174494 A174495 * A174497 A174498 A174499

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 17 2010

STATUS

approved

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Last modified March 20 21:07 EDT 2023. Contains 361391 sequences. (Running on oeis4.)