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A245249
E.g.f. satisfies: A'(x) = (1 + x*A(x))^7 with A(0)=1.
5
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
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
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jul 15 2014
STATUS
approved