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%I #8 Feb 24 2022 02:16:33
%S 1,1,2,3,6,35,285,2044,13804,108093,1083405,12281896,143452386,
%T 1763156031,23845410407,353626471808,5579871336488,92609430408361,
%U 1627509065584185,30379312334903408,598533509334403470,12366674489588950555,267527916985316556019
%N Expansion of e.g.f. 1 / (1 - x)^sech(x).
%F a(0) = 1; a(n) = -Sum_{k=1..n} (-1)^k * binomial(n-1,k-1) * A009435(k) * a(n-k).
%F a(n) ~ n! / (Gamma(1/cosh(1)) * n^(1 - 1/cosh(1))). - _Vaclav Kotesovec_, Feb 24 2022
%t nmax = 22; CoefficientList[Series[1/(1 - x)^Sech[x], {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(1/(1-x)^(1/cosh(x)))) \\ _Michel Marcus_, Feb 23 2022
%Y Cf. A009197, A009435, A351881, A351882.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Feb 23 2022
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