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A190948
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Numerator of Sum(binomial(n,k)*(-1)^k/(k^2+1),k=0..n).
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1
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1, 1, 1, 0, -12, -54, -2628, -77616, -86688, -3837456, -6295968, -5189982336, -773398378368, -60614059968, -710855139456, -274917009540096, -70812306032928768, -20799092342375424, -53842565061863424, -48391925819124400128, -3845848802828440117248, -64663161151688486424576, -30966053952082739476783104
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OFFSET
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0,5
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REFERENCES
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Flajolet, Philippe; and Sedgewick, Robert; Mellin transforms and asymptotics: finite differences and Rice's integrals. Theoret. Comput. Sci. 144 (1995), 101-124.
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LINKS
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Table of n, a(n) for n=0..22.
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EXAMPLE
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1, 1/2, 1/5, 0, -12/85, -54/221, -2628/8177, -77616/204425, -86688/204425, ...
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MAPLE
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T:=n->add(binomial(n, k)*(-1)^k/(k^2+1), k=0..n);
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MATHEMATICA
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Table[Sum[(Binomial[n, k](-1)^k)/(k^2+1), {k, 0, n}], {n, 0, 30}]//Numerator (* Harvey P. Dale, Jul 25 2020 *)
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CROSSREFS
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Cf. A190950.
Sequence in context: A137938 A009726 A230920 * A275249 A143856 A207102
Adjacent sequences: A190945 A190946 A190947 * A190949 A190950 A190951
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KEYWORD
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sign,frac
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AUTHOR
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N. J. A. Sloane, May 24 2011
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STATUS
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approved
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