A235131 E.g.f. 1/(1 - tan(2*x))^(1/2).

1, 1, 3, 23, 201, 2401, 33723, 564983, 10832721, 235620481, 5715989043, 153231400343, 4495861836441, 143343873560161, 4934418832685163, 182409363179578103, 7206898465033427361, 303073359560984509441, 13516205633151976330083, 637174194752117499594263

Offset: 0

Author

Vaclav Kotesovec, Jan 03 2014

Keywords

• nonn
• easy

Comments

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

Crossrefs

Cf. A000828 (p=1), A235132 (p=3).

Programs

Mathematica

CoefficientList[Series[1/(1 - Tan[2*x])^(1/2), {x, 0, 20}], x] * Range[0, 20]!

Formula

a(n) ~ n! * 2^(3*n+1/2) / (Pi^(n+1) * sqrt(n)).