A013559 Numerator of [x^n] in the Taylor expansion of exp(cosech(x)-coth(x)).

1, -1, 1, 1, -7, 1, 97, -55, -2063, 143, 17803, -968167, -250781, 7000033, -166831871, -571772647, 43685848289, 843598411471, -447550424579, -1263845119891, 84677077231169, 740683182137153, -11657476758734011, -474904166544135457, 28924058075775365981, -2379183287545454197

Offset: 0

Author

Patrick Demichel (patrick.demichel(AT)hp.com)

Keywords

• sign

Comments

The inner function is cosech(x)-coth(x) = -x/2 +x^3/24 -x^5/240 +17*x^7/40320 -31*x^9/725760 +691*x^11/159667200 -... with e.g.f numerators cosech(x)-coth(x) = sum b(n)x^n/(n+1)! apparently in A001469.

Examples

			1-x/2 +x^2/8 +x^3/48 -7*x^4/384 +x^5/1280 +97*x^6/46080 -...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A013521, A096664 (bisections?)

Programs

Maple

S:= series(exp(csch(x)-coth(x)),x,51):
seq(numer(coeff(S,x,j)),j=0..50); # Robert Israel, Nov 14 2016

Mathematica

Numerator[Take[CoefficientList[Series[Exp[Csch[x] - Coth[x]], {x,0,40}], x], {1, -1, 1}]] (* G. C. Greubel, Nov 13 2016 *)

Extensions

Name edited by R. J. Mathar, Dec 22 2011