Lehmer's Second Interesting Series(2)
A180875 に載せた式を確認してみる。
(01:34) gp > N=20; x='x+O('x^N);
(01:35) gp > Vec(serlaplace(2*(asin(exp(x/2)/sqrt(2))-Pi/4)*sqrt(exp(x)/(2-exp(x))^3)+exp(x)/(2-exp(x))))
%2 = [1.0000000000000000000000000000000000000, 3.0000000000000000000000000000000000000, 11.000000000000000000000000000000000000, 55.000000000000000000000000000000000000, 355.00000000000000000000000000000000000, 2807.0000000000000000000000000000000000, 26259.000000000000000000000000000000000, 283623.00000000000000000000000000000000, 3473315.0000000000000000000000000000000, 47552791.000000000000000000000000000000, 719718067.00000000000000000000000000000, 11932268231.000000000000000000000000000, 215053088835.00000000000000000000000000, 4186305575415.0000000000000000000000000, 87534887434835.000000000000000000000000, 1956680617267879.0000000000000000000000, 46561960552921315.000000000000000000000, 1175204650272267479.0000000000000000000, 31357650670190565363.000000000000000000, 881958890078887314567.00000000000000000]
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