A331405 - OEIS

%I #9 Jan 28 2020 06:29:40

%S 1,2,-8,-112,2176,71936,-3163136,-196237312,15258124288,1531746516992,

%T -185088737017856,-27405687884087296,4747122204712370176,

%U 973473732763710390272,-228670532983871365971968,-62056343388674412796444672,18982531521384459634512756736

%N 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.

%H Vaclav Kotesovec, <a href="/A331405/b331405.txt">Table of n, a(n) for n = 0..248</a>

%F 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

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

%Y Cf. A000182, A202038.

%K sign

%O 0,2

%A _Ilya Gutkovskiy_, Jan 16 2020