A009569 Expansion of e.g.f. sinh(log(1+tan(x))).

0, 1, -1, 5, -20, 136, -976, 8840, -88640, 1019776, -12933376, 181318400, -2767631360, 45821372416, -816582578176, 15596531778560, -317710534983680, 6876972491309056, -157606194409701376, 3812752893951672320, -97090584769337753600, 2596013487025352605696

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..430

Programs

Mathematica

CoefficientList[Series[(Tan[x]*(2 + Tan[x]))/(2*(1 + Tan[x])), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)
With[{nmax = 50}, CoefficientList[Series[Sinh[Log[1 + Tan[x]]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jan 21 2018 *)

PARI

x='x+O('x^30); concat([0], Vec(serlaplace(sinh(log(1+tan(x)))))) \\ G. C. Greubel, Jan 21 2018

Formula

a(n) ~ n! * (-1)^(n+1) * 4^n / Pi^(n+1). - Vaclav Kotesovec, Jan 23 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Terms a(20) and a(21) added by G. C. Greubel, Jan 21 2018