# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a222412
Showing 1-1 of 1

%I A222412 #36 Apr 24 2022 20:44:22
%S A222412 1,4,32,384,10240,40960,61931520,49545216,7927234560,475634073600,
%T A222412 1993133260800,177167400960,48753634065776640,195014536263106560,
%U A222412 39002907252621312000,842462796656620339200,2204424056667635712000,79359266040034885632000
%N A222412 Denominators in Taylor series expansion of (x/(exp(x) - 1))^(3/2)*exp(x/2).
%H A222412 Alois P. Heinz, <a href="/A222412/b222412.txt">Table of n, a(n) for n = 0..300</a>
%H A222412 David Broadhurst, <a href="/A241885/a241885.txt">Relations between A241885/A242225, A222411/A222412, and A350194/A350154.</a>
%H A222412 F. J. Dyson, N. E. Frankel and M. L. Glasser, <a href="http://arxiv.org/abs/1009.4274">Lehmer's Interesting Series</a>, arXiv:1009.4274 [math-ph], 2010-2011.
%H A222412 F. J. Dyson, N. E. Frankel and M. L. Glasser, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.120.02.116">Lehmer's interesting series</a>, Amer. Math. Monthly, 120 (2013), 116-130.
%H A222412 D. H. Lehmer, <a href="https://www.jstor.org/stable/2322496">Interesting series involving the central binomial coefficient</a>, Amer. Math. Monthly, 92(7) (1985), 449-457.
%F A222412 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).
%e A222412 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
%p A222412 gf:= (x/(exp(x)-1))^(3/2)*exp(x/2):
%p A222412 a:= n-> denom(coeff(series(gf, x, n+3), x, n)):
%p A222412 seq(a(n), n=0..25);  # _Alois P. Heinz_, Mar 02 2013
%t A222412 Series[(x/(Exp[x]-1))^(3/2)*Exp[x/2], {x, 0, 25}] // CoefficientList[#, x]& // Denominator (* _Jean-François Alcover_, Mar 18 2014 *)
%Y A222412 Cf. A222411.
%Y A222412 Cf. also A241885/A242225, A350194/A350154.
%K A222412 nonn,frac
%O A222412 0,2
%A A222412 _N. J. A. Sloane_, Feb 28 2013

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE