A235128 E.g.f. 1/(1 - sin(7*x))^(1/7).

1, 1, 8, 71, 1072, 20161, 476288, 13315751, 432387712, 15959926081, 660372282368, 30265936565831, 1522069164439552, 83327826089289601, 4933286107483701248, 314052936209639958311, 21392225375507849838592, 1552501782546292090638721, 119588747474281844162428928

Offset

0,3

Comments

Generally, for e.g.f. 1/(1-sin(p*x))^(1/p) we have a(n) ~ n! * 2^(n+3/p) * p^n / (Gamma(2/p) * n^(1-2/p) * Pi^(n+2/p)).

Links

Table of n, a(n) for n=0..18.

Formula

a(n) ~ n! * 2^(n+3/7) * 7^n / (Gamma(2/7) * n^(5/7) * Pi^(n+2/7)).

Mathematica

CoefficientList[Series[1/(1-Sin[7*x])^(1/7), {x, 0, 20}], x] * Range[0, 20]!

Crossrefs

Cf. A001586 (p=2), A007788 (p=3), A144015 (p=4), A230134 (p=5), A227544 (p=6), A230114 (p=8).

Sequence in context: A094911 A294166 A203008 * A226163 A338622 A004165

Adjacent sequences: A235125 A235126 A235127 * A235129 A235130 A235131

Keyword

nonn,easy

Author

Vaclav Kotesovec, Jan 03 2014

Status

approved