A352164 Expansion of e.g.f. 1/(cosh(x) - tanh(x)).

1, 1, 1, -2, -23, -104, -119, 3088, 37297, 209536, -569039, -29795072, -376722983, -1715047424, 35167499641, 1004215072768, 12109139111137, -1945682345984, -3571363955938079, -84438462955323392, -825288198538588343, 12032890515685113856

Offset: 0

Author

Seiichi Manyama, Mar 06 2022

Keywords

• sign

Crossrefs

Cf. A000182, A011782, A352151.

Programs

Mathematica

m = 21; Range[0, m]! * CoefficientList[Series[1/(Cosh[x] - Tanh[x]), {x, 0, m}], x] (* Amiram Eldar, Mar 06 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(cosh(x)-tanh(x))))

PARI

c(n) = ((-4)^n-(-16)^n)*bernfrac(2*n)/(2*n);
b(n) = if(n%2==1, (-1)^((n+1)/2)*c((n+1)/2), 1);
a(n) = if(n==0, 1, -sum(k=1, n, b(k)*binomial(n, k)*a(n-k)));

Formula

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.