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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
1, 2, -8, -112, 2176, 71936, -3163136, -196237312, 15258124288, 1531746516992, -185088737017856, -27405687884087296, 4747122204712370176, 973473732763710390272, -228670532983871365971968, -62056343388674412796444672, 18982531521384459634512756736
OFFSET
0,2
LINKS
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
MATHEMATICA
nmax = 16; CoefficientList[Series[1/(1 + ContinuedFractionK[(-1)^k k (k + 1) x, 1, {k, 1, nmax}]), {x, 0, nmax}], x]
CROSSREFS
Sequence in context: A012665 A317076 A211938 * A005787 A012343 A012347
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jan 16 2020
STATUS
approved