A245249 E.g.f. satisfies: A'(x) = (1 + x*A(x))^7 with A(0)=1.

1, 1, 7, 56, 609, 8960, 162015, 3455760, 85499505, 2407507200, 75954495015, 2654662651200, 101833013541105, 4253509461922560, 192174397814079135, 9338303873329240320, 485654062232697912225, 26915598265961374986240, 1583628181230906140008455

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..265

Formula

E.g.f. satisfies: A(x) = 1 + Integral (1 + x*A(x))^7 dx.

a(n) ~ c * d^n * n! / n^(5/6), where d = 3.4216107680..., c = 0.68714396...

Prog

(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal((1+x*A+x*O(x^n))^7)); 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), A245247 (p=5), A245248 (p=6).

Sequence in context: A259900 A087751 A099345 * A110830 A304691 A218428

Adjacent sequences: A245246 A245247 A245248 * A245250 A245251 A245252

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jul 15 2014

Status

approved