A009753 Expansion of tan(x)/(1+x).

0, 1, -2, 8, -32, 176, -1056, 7664, -61312, 559744, -5597440, 61925632, -743107584, 9682766848, -135558735872, 2035284795392, -32564556726272, 553807329689600, -9968531934412800, 189431195638956032, -3788623912779120640

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..445

Crossrefs

Cf. A049471 (tan(1)).

Programs

Maple

G(x):= tan(x)/(1+x): f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=0..20); # Zerinvary Lajos, Apr 03 2009

Mathematica

CoefficientList[Series[Tan[x]/(1 + x), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 24 2015 *)

PARI

x='x+O('x^30); concat([0], Vec(serlaplace(tan(x)/(1+x)))) \\ G. C. Greubel, Feb 12 2018

Formula

a(n) ~ n! * (-1)^(n+1) * tan(1). - Vaclav Kotesovec, Jan 24 2015

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997