A009113 Expansion of e.g.f. cos(x)/exp(sinh(x)).

1, -1, 0, 1, 0, 3, -24, 61, -256, 1383, -5632, 28345, -156032, 808299, -4761600, 28955317, -178225152, 1188919631, -8081772544, 56978370417, -422364381184, 3196912985683, -25184814366720, 205147130407981, -1713906141986816

Offset: 0

Author

R. H. Hardin

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Programs

Magma

m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x)/Exp(Sinh(x)))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 26 2018

Mathematica

With[{nmax = 30}, CoefficientList[Series[Cos[x]/Exp[Sinh[x]], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jul 26 2018 *)

PARI

x='x+O('x^30); Vec(serlaplace(cos(x)/exp(sinh(x)))) \\ G. C. Greubel, Jul 26 2018

Extensions

Extended with signs by Olivier Gérard, Mar 15 1997