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A222411 Numerators in Taylor series expansion of (x/(exp(x) - 1))^(3/2)*exp(x/2). 3
1, -1, -1, 5, 7, -19, -869, 715, 2339, -200821, -12863, 2117, 7106149, -64604977, -131301607, 7629931291, 174053933, -19449462373, -46949081169401, 355455588729389, 10635113572583999, -6511303438681407901, -349640201588122693, 9112944418860287 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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-> numer(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]& // Numerator (* Jean-Fran├žois Alcover, Mar 18 2014 *)

CROSSREFS

Cf. A222412 (denominators).

Sequence in context: A062654 A231865 A130729 * A274022 A117321 A279252

Adjacent sequences:  A222408 A222409 A222410 * A222412 A222413 A222414

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Feb 28 2013

STATUS

approved

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Last modified August 8 06:27 EDT 2020. Contains 336290 sequences. (Running on oeis4.)