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A222411
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Numerators in Taylor series expansion of (x/(exp(x) - 1))^(3/2)*exp(x/2).
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7
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1, -1, -1, 5, 7, -19, -869, 715, 2339, -200821, -12863, 2117, 7106149, -64604977, -131301607, 7629931291, 174053933, -19449462373, -46949081169401, 355455588729389, 10635113572583999, -6511303438681407901, -349640201588122693, 9112944418860287
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OFFSET
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0,4
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..300
David Broadhurst, Relations between A241885/A242225, A222411/A222412, and A350194/A350154.
F. J. Dyson, N. E. Frankel and M. L. Glasser, Lehmer's Interesting Series, arXiv:1009.4274 [math-ph], 2010-2011.
F. J. Dyson, N. E. Frankel and M. L. Glasser, Lehmer's interesting series, Amer. Math. Monthly, 120 (2013), 116-130.
D. H. Lehmer, Interesting series involving the central binomial coefficient, Amer. Math. Monthly, 92(7) (1985), 449-457.
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FORMULA
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Theorem: A241885(n)/A242225(n) = n!*A222411(n)/(A222412(n)*(-1)^n/(1-2*n)) = n!*A350194(n)/(A350154(n)*(2*n+1)). - David Broadhurst, Apr 23 2022 (see Link).
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EXAMPLE
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The first few fractions are 1, -1/4, -1/32, 5/384, 7/10240, -19/40960, -869/61931520, 715/49545216, ... = A222411/A222412. - Petros Hadjicostas, May 14 2020
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MAPLE
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gf:= (x/(exp(x)-1))^(3/2)*exp(x/2):
a:= n-> numer(coeff(series(gf, x, n+3), x, n)):
seq(a(n), n=0..25); # Alois P. Heinz, Mar 02 2013
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MATHEMATICA
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Series[(x/(Exp[x]-1))^(3/2)*Exp[x/2], {x, 0, 25}] // CoefficientList[#, x]& // Numerator (* Jean-François Alcover, Mar 18 2014 *)
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CROSSREFS
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Cf. A222412 (denominators).
Cf. also A241885/A242225, A350194/A350154.
Sequence in context: A062654 A231865 A130729 * A274022 A117321 A279252
Adjacent sequences: A222408 A222409 A222410 * A222412 A222413 A222414
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KEYWORD
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sign,frac
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AUTHOR
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N. J. A. Sloane, Feb 28 2013
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STATUS
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approved
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