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A222412 Denominators in Taylor series expansion of (x/(exp(x) - 1))^(3/2)*exp(x/2). 3
1, 4, 32, 384, 10240, 40960, 61931520, 49545216, 7927234560, 475634073600, 1993133260800, 177167400960, 48753634065776640, 195014536263106560, 39002907252621312000, 842462796656620339200, 2204424056667635712000, 79359266040034885632000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..300

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.

EXAMPLE

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

MAPLE

gf:= (x/(exp(x)-1))^(3/2)*exp(x/2):

a:= n-> denom(coeff(series(gf, x, n+3), x, n)):

seq(a(n), n=0..25);  # Alois P. Heinz, Mar 02 2013

MATHEMATICA

Series[(x/(Exp[x]-1))^(3/2)*Exp[x/2], {x, 0, 25}] // CoefficientList[#, x]& // Denominator (* Jean-Fran├žois Alcover, Mar 18 2014 *)

CROSSREFS

Cf. A222411.

Sequence in context: A303049 A047053 A201594 * A007763 A195193 A203435

Adjacent sequences:  A222409 A222410 A222411 * A222413 A222414 A222415

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Feb 28 2013

STATUS

approved

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Last modified July 11 20:03 EDT 2020. Contains 335652 sequences. (Running on oeis4.)