A331405 G.f.: 1/(1 - 1*2*x/(1 + 2*3*x/(1 - 3*4*x/(1 + 4*5*x/(1 - 5*6*x/(1 + ...)))))), a continued fraction.

1, 2, -8, -112, 2176, 71936, -3163136, -196237312, 15258124288, 1531746516992, -185088737017856, -27405687884087296, 4747122204712370176, 973473732763710390272, -228670532983871365971968, -62056343388674412796444672, 18982531521384459634512756736

Offset: 0

Author

Ilya Gutkovskiy, Jan 16 2020

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..248

Crossrefs

Cf. A000182, A202038.

Programs

Mathematica

nmax = 16; CoefficientList[Series[1/(1 + ContinuedFractionK[(-1)^k k (k + 1) x, 1, {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

a(n) ~ sin((2*n+1)*Pi/4) * 2^(6*n + 8) * Pi^(n + 3/2) * n^(2*n + 3/2) / (exp(2*n) * Gamma(1/4)^(4*n + 4)). - Vaclav Kotesovec, Jan 28 2020