A351883 Expansion of e.g.f. 1 / (1 - x)^sech(x).
1, 1, 2, 3, 6, 35, 285, 2044, 13804, 108093, 1083405, 12281896, 143452386, 1763156031, 23845410407, 353626471808, 5579871336488, 92609430408361, 1627509065584185, 30379312334903408, 598533509334403470, 12366674489588950555, 267527916985316556019
Offset: 0
Keywords
Programs
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Mathematica
nmax = 22; CoefficientList[Series[1/(1 - x)^Sech[x], {x, 0, nmax}], x] Range[0, nmax]! -
PARI
my(x='x+O('x^30)); Vec(serlaplace(1/(1-x)^(1/cosh(x)))) \\ Michel Marcus, Feb 23 2022
Formula
a(0) = 1; a(n) = -Sum_{k=1..n} (-1)^k * binomial(n-1,k-1) * A009435(k) * a(n-k).
a(n) ~ n! / (Gamma(1/cosh(1)) * n^(1 - 1/cosh(1))). - Vaclav Kotesovec, Feb 24 2022