A009769 Expansion of tanh(log(1+1/x)).

1, 0, -4, 24, -96, 0, 5760, -80640, 645120, 0, -116121600, 2554675200, -30656102400, 0, 11158821273600, -334764638208000, 5356234211328000, 0, -3278015337332736000, 124564582818643968000, -2491291656372879360000, 0

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

E.g.f.: (2*x+1)/(2*x^2+2*x+1) = 1-4*x^2/2!+24*x^3/3!-96*x^4/4!+....

Recurrence: a(n) = -2*n*a(n-1)-2*n*(n-1)*a(n-2), a(0) = 1, a(1) = 0.

a(n) = -n!/2*((-1+i)^(n+1) + (-1-i)^(n+1)) = -n!*sqrt(2)^(n+1)* cos(3*Pi*(n+1)/4).

a(n) = 2^n*A009014(n). a(n) = -n!*A009116(n+1).

For x > -1/2 we have (2*x+1)/(2*x^2+2*x+1) = 2*int {t = 0..inf} exp(-t*(2*x+1))*cos(t). Using this we obtain a(n) = 2*(-2)^n*int {t = 0..inf} t^n*exp(-t)*cos(t). - Peter Bala, Oct 05 2011

Mathematica

nn = 26; Range[0, nn]! CoefficientList[Series[Tanh[Log[1 + 1/x]], {x, 0, nn}], x] (* T. D. Noe, Oct 05 2011 *)

Crossrefs

Cf. A009014, A009116.

Sequence in context: A222670 A225681 A259814 * A119878 A054603 A100381

Adjacent sequences: A009766 A009767 A009768 * A009770 A009771 A009772

Keyword

sign,easy

Author

R. H. Hardin

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997

Status

approved