A235132 E.g.f. 1/(1 - tan(3*x))^(1/3).

1, 1, 4, 46, 568, 9976, 203104, 4995136, 140343808, 4493656576, 160609429504, 6356981099776, 275688520680448, 13008983675954176, 663382602064482304, 36360098005522825216, 2131554196360938815488, 133093201551208236875776, 8818123347826691244949504

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) * n^((1-p)/p) * p^n / (Pi^(n+1/p) * Gamma(1/p)).

Crossrefs

Cf. A000828 (p=1), A235131 (p=2).

Programs

Mathematica

CoefficientList[Series[1/(1 - Tan[3*x])^(1/3), {x, 0, 20}], x] * Range[0, 20]!

Formula

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