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A245247 E.g.f. satisfies: A'(x) = (1 + x*A(x))^5 with A(0)=1. 5
1, 1, 5, 30, 255, 2880, 39495, 640800, 12048225, 257203200, 6146830125, 162636676800, 4719436701375, 149035892832000, 5088353594517375, 186769650799200000, 7334368923555410625, 306830158711872000000, 13623286425863528263125, 639832207565577018240000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

In general, if e.g.f satisfies A'(x) = (1+x*A(x))^p, then a(n) ~ c(p) * d(p)^n * n! / n^(1-1/(p-1)), where c(p) and d(p) are constants independent on n.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..290

FORMULA

E.g.f. satisfies: A(x) = 1 + Integral (1 + x*A(x))^5 dx.

a(n) ~ c * d^n * n! / n^(3/4), where d = 2.56982683907..., c = 0.803451595...

PROG

(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal((1+x*A+x*O(x^n))^5)); n!*polcoeff(A, n)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A006882(n-1) (p=1), A000142 (p=2), A144008 (p=3), A144009 (p=4), A245248 (p=6), A245249 (p=7).

Sequence in context: A257741 A308946 A279155 * A199131 A277464 A258300

Adjacent sequences:  A245244 A245245 A245246 * A245248 A245249 A245250

KEYWORD

nonn,easy

AUTHOR

Vaclav Kotesovec, Jul 15 2014

STATUS

approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)