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A109577 E.g.f.: 2x/[1-exp(-2x)+2exp(-x)]. 0
0, 1, 0, 3, -12, 65, -450, 3577, -32424, 331137, -3757350, 46892681, -638447436, 9416929249, -149581289130, 2545707159465, -46213451575248, 891368532889601, -18204123410896590, 392431030262264329, -8904987308885931060, 212174197452256551393, -5296088301994320448530 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..22.

FORMULA

E.g.f.: (2*x)/(1-exp(-2*x)+2*exp(-x))=2*x/(1 +2*G(0)) ; G(k)= 1-(2^k)/(2-4*x/(2*x+(2^k)*(k+1)/G(k+1))); (continued fraction Euler's kind, 1-step ). - Sergei N. Gladkovskii, Jan 08 2012

a(n) ~ n! * (-1)^(n+1) * (1-1/sqrt(2))/log(1+sqrt(2))^n. - Vaclav Kotesovec, Sep 26 2013

MAPLE

G:=2*x/(1-exp(-2*x)+2*exp(-x)): Gser:=series(G, x=0, 26): 0, seq(n!*coeff(Gser, x^n), n=1..23); # yields the signed sequence

MATHEMATICA

g[x_] = x/(-1 + Exp[ -2*x] - 2*Exp[ -x]) h[x_, n_] = Dt[g[x], {x, n}] a[x_] = Table[h[x, n], {n, 0, 50}]; b = 2*a[0]

CROSSREFS

Sequence in context: A216373 A200309 A256124 * A242575 A144297 A007017

Adjacent sequences:  A109574 A109575 A109576 * A109578 A109579 A109580

KEYWORD

sign

AUTHOR

Roger L. Bagula, Jun 28 2005

STATUS

approved

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Last modified June 24 23:16 EDT 2021. Contains 345445 sequences. (Running on oeis4.)