The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A245248 E.g.f. satisfies: A'(x) = (1 + x*A(x))^6 with A(0)=1. 5
1, 1, 6, 42, 408, 5328, 84960, 1600128, 34957440, 868247424, 24152048640, 744116855040, 25155056424960, 925729237969920, 36842642690181120, 1576774342552872960, 72212210263605657600, 3523820406525504552960, 182532196288859620147200, 10003033225361632653803520 (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
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
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Jul 15 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 16:48 EDT 2024. Contains 372916 sequences. (Running on oeis4.)