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

0,4

Links

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

Formula

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

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 *)

Prog

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

Crossrefs

Sequence in context: A318250 A337292 A024066 * A061964 A133667 A354848

Adjacent sequences: A009566 A009567 A009568 * A009570 A009571 A009572

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

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

Status

approved