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Search: id:A109573
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| A109573 |
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E.g.f.: 2x/[1+exp(-2x)]. |
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+0
1
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| 0, 1, 2, 0, -8, 0, 96, 0, -2176, 0, 79360, 0, -4245504, 0, 313155584, 0, -30460116992, 0, 3777576173568, 0, -581777702256640, 0, 108932957168730112, 0, -24370173276164456448, 0, 6419958484945407574016, 0, -1967044844910430876860416, 0, 693575525634287935244206080, 0
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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"Bernoulli numbers" for 2x/[1+exp(-2x)].
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FORMULA
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a(0) = 0 and for n > 0 a(n) = n 2^(n-1) E_{n-1}(1) where E_{m}(x) are the Euler polynomials. [From Peter Luschny (peter(AT)luschny.de), Jan 26 2009]
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MAPLE
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G:=2*x/(1+exp(-2*x)): Gser:=series(G, x=0, 35): 0, seq(n!*coeff(Gser, x^n), n=1..32); # yields the signed sequence
A109573 := n -> `if`(n = 0, 0, n*2^(n-1)*euler(n-1, 1)): [From Peter Luschny (peter(AT)luschny.de), Jan 26 2009]
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MATHEMATICA
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g[x_] = x/(-1 + Sum[(-2)^(n - 1)*x^n/n!, {n, 1, Infinity}]) h[x_, n_] = Dt[g[x], {x, n}] a[x_] = Table[h[x, n], {n, 0, 50}]; b = Abs[a[0]]
X[m_] := m Sum[(-2)^(m-1-k) k! StirlingS2[m-1, k], {k, 0, m-1}]; Table[X[i], {i, 0, 20}] [From Peter Luschny (peter(AT)luschny.de), Apr 29 2009]
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CROSSREFS
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Sequence in context: A167029 A094030 A103424 this_sequence A159810 A146543 A021052
Adjacent sequences: A109570 A109571 A109572 this_sequence A109574 A109575 A109576
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KEYWORD
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sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 27 2005
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