A245247 E.g.f. satisfies: A'(x) = (1 + x*A(x))^5 with A(0)=1.

1, 1, 5, 30, 255, 2880, 39495, 640800, 12048225, 257203200, 6146830125, 162636676800, 4719436701375, 149035892832000, 5088353594517375, 186769650799200000, 7334368923555410625, 306830158711872000000, 13623286425863528263125, 639832207565577018240000

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: A308946 A346681 A279155 * A353547 A199131 A342389

Adjacent sequences: A245244 A245245 A245246 * A245248 A245249 A245250

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jul 15 2014

Status

approved