This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A008991 #33 Feb 16 2025 08:32:32 %S A008991 1,-1,1,-1,-67,-1,-64397,-113249,-3679787,-810304169,-6040635661561, %T A008991 -428305999661,-16827172241810597,-5620292762592913, %U A008991 -1550760014054450957,-4168373361283100017,-8551022502876237590534947 %N A008991 Numerators of coefficients in expansion of sqrt(sin(x)/x) (even powers only). %H A008991 G. C. Greubel, <a href="/A008991/b008991.txt">Table of n, a(n) for n = 0..255</a> %H A008991 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SincFunction.html">The Sinc Function</a>. %F A008991 sum(n>=0, A008991(n)/A008992(n) ) = A117017 - _Johannes W. Meijer_, Feb 10 2013 %p A008991 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 %t A008991 Numerator[CoefficientList[Series[Sqrt[Sin[x]/x], {x, 0, 50}], x][[1 ;; -1 ;; 2]]] (* _G. C. Greubel_, Jul 21 2018 *) %o A008991 (Sage) %o A008991 length = 16; T = taylor(sqrt(sin(x)/x),x,0,2*length+2) %o A008991 [T.coefficient(x, 2*n).numerator() for n in (0..length)] %o A008991 # _Peter Luschny_, Dec 13 2012 %Y A008991 Denominators are in A008992. %Y A008991 Appears in A220002 and A220466. %K A008991 sign %O A008991 0,5 %A A008991 _N. J. A. Sloane_