A222411 - OEIS

A222411

Numerators in Taylor series expansion of (x/(exp(x) - 1))^(3/2)*exp(x/2).

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

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.

FORMULA

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).

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-François Alcover, Mar 18 2014 *)

CROSSREFS

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

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Feb 28 2013

STATUS

approved