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 A002676 M4282 N1789 #32 Feb 16 2025 08:32:26
%S A002676 1,6,80,30240,1814400,2661120,871782912000,3138418483200,
%T A002676 84687482880000,170303140572364800,1124000727777607680000,
%U A002676 724146127139635200000,12703681025488077520896000000,76222086152928465125376000000,1531041037877004667453440000000
%N A002676 Denominators of coefficients for central differences M_{4}^(2*n).
%C A002676 From _Peter Bala_, Oct 03 2019: (Start)
%C A002676 Denominators in the expansion of (2*sinh(x/2))^4 = x^4 + (1/6)*x^6 + (1/80)*x^8 + (17/30240)*x^10 + ....
%C A002676 Let f(x) be a polynomial in x. The expansion of (2*sinh(x/2))^4 leads to a formula for the fourth central differences: f(x+2) - 4*f(x+1) + 6*f(x) - 4*f(x-1) + f(x-2) = (2*sinh(D/2))^4(f(x)) = D^4(f(x)) + (1/6)*D^6(f(x)) + (1/80)*D^8(f(x)) + (17/30240)*D^10(f(x)) + ..., where D denotes the differential operator d/dx. (End)
%D A002676 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002676 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002676 H. E. Salzer, <a href="https://doi.org/10.1002/sapm1963421162">Tables of coefficients for obtaining central differences from the derivatives</a>, Journal of Mathematics and Physics (this journal is also called Studies in Applied Mathematics), 42 (1963), 162-165, plus several inserted tables.
%H A002676 H. E. Salzer, <a href="/A002675/a002675.png">Annotated scanned copy of left side of Table II</a>.
%H A002676 E. W. Weisstein, <a href="https://mathworld.wolfram.com/CentralDifference.html">Central Difference</a>. From MathWorld--A Wolfram Web Resource.
%F A002676 a(n) = denominator(4! * m(4, 2 * n) / (2 * n)!) where m(k, q) is defined in A002672. - _Sean A. Irvine_, Dec 20 2016
%p A002676 gf := 6 - 8*cosh(sqrt(x)) + 2*cosh(2*sqrt(x)): ser := series(gf, x, 40):
%p A002676 seq(denom(coeff(ser,x,n)), n=2..16); # _Peter Luschny_, Oct 05 2019
%Y A002676 Cf. A002675 (numerators). Cf. A002671, A002672, A002673, A002674, A002677.
%K A002676 nonn,frac
%O A002676 2,2
%A A002676 _N. J. A. Sloane_
%E A002676 More terms from _Sean A. Irvine_, Dec 20 2016