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A132094
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Numerators of expansion of e.g.f. x^2/(2*(cos(x)-1)), even powers only.
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7
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-1, -1, -1, -5, -7, -15, -7601, -91, -3617, -745739, -3317609, -5981591, -5436374093, -213827575, -213745149261, -249859397004145, -238988952277727, -28354566442037, -26315271553053477373, -108409774812137683, -3394075340453838586663, -62324003400640902910331
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OFFSET
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1,4
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COMMENTS
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Numerators and denominators given only for even n (odd n have numerators = 0).
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REFERENCES
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J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199. See Table 3.3.
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LINKS
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FORMULA
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Asymptotic series 2*Psi(1,x) + x*Psi(2,x) ~ Sum_{n>=1} (-1)^n* a(n)/(A132095(n)*x^(2*n-1)) as x -> oo. - Robert Israel, May 27 2015
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EXAMPLE
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-1, 0, -1/6, 0, -1/10, 0, -5/42, 0, -7/30, 0, -15/22, 0, -7601/2730, 0.
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MAPLE
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A132094 := proc(n) add( 2*(-1)^i*x^(2*i)/(2*i+2)!, i=0..n+1) ; numer(coeftayl(-1/%, x=0, n)*n!) ; end: for n from 0 to 46 by 2 do printf("%d, ", A132094(n)) ; od: # R. J. Mathar, Oct 18 2007
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MATHEMATICA
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A132094[n_] := (s = Sum[ 2*(-1)^i*x^(2*i)/(2*i + 2)!, {i, 0, n + 1}]; Numerator[SeriesCoefficient[-1/s, {x, 0, n}]*n!]);
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PROG
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(PARI) my(x='x+O('x^50), v=apply(numerator, Vec(serlaplace(x^2/(2*(cos(x)-1)))))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Jan 25 2024
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CROSSREFS
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KEYWORD
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frac,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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