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%I #14 Mar 06 2022 23:07:56
%S 1,1,1,-2,-23,-104,-119,3088,37297,209536,-569039,-29795072,
%T -376722983,-1715047424,35167499641,1004215072768,12109139111137,
%U -1945682345984,-3571363955938079,-84438462955323392,-825288198538588343,12032890515685113856
%N Expansion of e.g.f. 1/(cosh(x) - tanh(x)).
%F a(0) = 1; a(n) = -Sum_{k=1..n} b(k) * binomial(n,k) * a(n-k), where b(k) = (-1)^((k+1)/2) * A000182((k+1)/2) if k is odd, otherwise 1.
%t m = 21; Range[0, m]! * CoefficientList[Series[1/(Cosh[x] - Tanh[x]), {x, 0, m}], x] (* _Amiram Eldar_, Mar 06 2022 *)
%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(cosh(x)-tanh(x))))
%o (PARI) c(n) = ((-4)^n-(-16)^n)*bernfrac(2*n)/(2*n);
%o b(n) = if(n%2==1, (-1)^((n+1)/2)*c((n+1)/2), 1);
%o a(n) = if(n==0, 1, -sum(k=1, n, b(k)*binomial(n, k)*a(n-k)));
%Y Cf. A000182, A011782, A352151.
%K sign
%O 0,4
%A _Seiichi Manyama_, Mar 06 2022
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