A245248 E.g.f. satisfies: A'(x) = (1 + x*A(x))^6 with A(0)=1.

1, 1, 6, 42, 408, 5328, 84960, 1600128, 34957440, 868247424, 24152048640, 744116855040, 25155056424960, 925729237969920, 36842642690181120, 1576774342552872960, 72212210263605657600, 3523820406525504552960, 182532196288859620147200, 10003033225361632653803520

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..300

Formula

E.g.f. satisfies: A(x) = 1 + Integral (1 + x*A(x))^6 dx.

a(n) ~ c * d^n * n! / n^(4/5), where d = 3.00663532009..., c = 0.73726997...

Prog

(PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal((1+x*A+x*O(x^n))^6)); 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), A245249 (p=7).

Sequence in context: A336950 A304071 A052608 * A197712 A306173 A254529

Adjacent sequences: A245245 A245246 A245247 * A245249 A245250 A245251

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jul 15 2014

Status

approved