A305708 Expansion of e.g.f. exp(cos(x)/exp(x) - 1).

1, -1, 1, 1, -11, 43, -83, -275, 3833, -21561, 51369, 375593, -5860147, 40452371, -101676235, -1409619211, 23912208945, -189650997937, 454996127889, 11250036170129, -204691511497499, 1799897065507003, -3741969787709699, -164548323889940675, 3183842522596250537, -30356999697044585833

Offset: 0

Author

Ilya Gutkovskiy, Jun 08 2018

Keywords

• sign

Examples

			exp(cos(x)/exp(x) - 1) = 1 - x + x^2/2! + x^3/3! - 11*x^4/4! + 43*x^5/5! - 83*x^6/6! - 275*x^7/7! + ...
		

Crossrefs

Cf. A004211, A009116, A009216, A009235, A009255, A009276, A146559, A155585.

Programs

Maple

a:=series(exp(cos(x)/exp(x)-1),x=0,26): seq(n!*coeff(a,x,n),n=0..25); # Paolo P. Lava, Mar 26 2019

Mathematica

nmax = 25; CoefficientList[Series[Exp[Cos[x]/Exp[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = Sum[Re[(-1 - I)^k] Binomial[n - 1, k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 25}]