A190948 Numerator of Sum_{k=0..n} binomial(n,k)*(-1)^k/(k^2+1).

1, 1, 1, 0, -12, -54, -2628, -77616, -86688, -3837456, -6295968, -5189982336, -773398378368, -60614059968, -710855139456, -274917009540096, -70812306032928768, -20799092342375424, -53842565061863424, -48391925819124400128, -3845848802828440117248, -64663161151688486424576, -30966053952082739476783104

Offset

0,5

Links

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

Philippe Flajolet and Robert Sedgewick, Mellin transforms and asymptotics: Finite differences and Rice's integrals, Theoretical Computer Science 144.1-2 (1995): 101-124.

Example

1, 1/2, 1/5, 0, -12/85, -54/221, -2628/8177, -77616/204425, -86688/204425, ...

Maple

T:=n->add(binomial(n, k)*(-1)^k/(k^2+1), k=0..n);

Mathematica

Table[Sum[(Binomial[n, k](-1)^k)/(k^2+1), {k, 0, n}], {n, 0, 30}]//Numerator (* Harvey P. Dale, Jul 25 2020 *)

Prog

(PARI) a(n) = numerator(sum(k=0, n, binomial(n, k)*(-1)^k/(k^2+1))); \\ Michel Marcus, Jan 08 2024

Crossrefs

Cf. A190950.

Sequence in context: A137938 A009726 A230920 * A275249 A143856 A207102

Adjacent sequences: A190945 A190946 A190947 * A190949 A190950 A190951

Keyword

sign,frac

Author

N. J. A. Sloane, May 24 2011

Status

approved