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A296940
Expansion of e.g.f. sech(x*tan(x/2)) (even powers only).
3
1, 0, -3, -15, 406, 14355, -189123, -42283696, -837846615, 284972761557, 28521503291230, -3070544172379761, -1054107683427761463, 1143265731049052000, 54900209444888714822181, 7959249060310612253252265, -3679623847504649619798598778, -1631286181830482909037469295781
OFFSET
0,3
FORMULA
a(n) = (2*n)! * [x^(2*n)] sech(x*tan(x/2)).
EXAMPLE
sech(x*tan(x/2)) = 1 - 3*x^4/4! - 15*x^6/6! + 406*x^8/8! + ...
MATHEMATICA
nmax = 17; Table[(CoefficientList[Series[Sech[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Dec 22 2017
STATUS
approved