A008991 Numerators of coefficients in expansion of sqrt(sin(x)/x) (even powers only).

1, -1, 1, -1, -67, -1, -64397, -113249, -3679787, -810304169, -6040635661561, -428305999661, -16827172241810597, -5620292762592913, -1550760014054450957, -4168373361283100017, -8551022502876237590534947

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..255
• Eric Weisstein's World of Mathematics, The Sinc Function.

Crossrefs

Denominators are in A008992.

Appears in A220002 and A220466.

Programs

Maple

A008991 := n -> numer(coeff(taylor(sqrt(sin(x)/x), x, 2*n+2), x, 2*n)):  seq(A008991(n), n=0..16); # Johannes W. Meijer, Feb 10 2013

Mathematica

Numerator[CoefficientList[Series[Sqrt[Sin[x]/x], {x, 0, 50}], x][[1 ;; -1 ;; 2]]] (* G. C. Greubel, Jul 21 2018 *)

Sage

length = 16; T = taylor(sqrt(sin(x)/x),x,0,2*length+2)
[T.coefficient(x, 2*n).numerator() for n in (0..length)]
# Peter Luschny, Dec 13 2012

Formula

sum(n>=0, A008991(n)/A008992(n) ) = A117017 - Johannes W. Meijer, Feb 10 2013