%I M5177 N2249 #32 Feb 27 2019 14:03:01

%S 1,24,5760,322560,51609600,13624934400,19837904486400,2116043145216,

%T 20720294477955072,15747423803245854720,131978409017679544320,

%U 72852081777759108464640,151532330097738945606451200,2828603495157793651320422400,19687080326298243813190139904000

%N Denominators of coefficients for numerical differentiation.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Ruperto Corso, <a href="/A002555/b002555.txt">Table of n, a(n) for n = 1..387</a>

%H W. G. Bickley and J. C. P. Miller, <a href="http://dx.doi.org/10.1080/14786444208521334">Numerical differentiation near the limits of a difference table</a>, Phil. Mag., 33 (1942), 1-12 (plus tables).

%H W. G. Bickley and J. C. P. Miller, <a href="/A002551/a002551.pdf">Numerical differentiation near the limits of a difference table</a>, Phil. Mag., 33 (1942), 1-12 (plus tables) [Annotated scanned copy]

%H T. R. Van Oppolzer, <a href="http://www.archive.org/stream/lehrbuchzurbahnb02oppo#page/23/mode/1up">Lehrbuch zur Bahnbestimmung der Kometen und Planeten</a>, Vol. 2, Engelmann, Leipzig, 1880, p. 23.

%F a(n) is the denominator of (-1)^(n-1)*Cn-1{1^2..(2n-1)^2}/((2n)!*2^(2n-3)), where Cn{1^2..(2n+1)^2} is equal to 1 when n=0, otherwise, it is the sum of the products of all possible combinations, of size n, of the numbers (2k+1)^2 with k=0,1,..,n. - _Ruperto Corso_, Dec 15 2011

%F a(n) = denominator(A001824(n-1)*(-1)^(n-1)/(2^(2*n-3)*(2*n)!)). - _Sean A. Irvine_, Mar 29 2014

%p with(combinat): a:=n->add(mul(k, k=j), j=choose([seq((2*i-1)^2, i=1..n)], n-1))*(-1)^(n-1)/(2^(2*n-3)*(2*n)!): seq(denom(a(n)), n=1..20); # _Ruperto Corso_, Dec 15 2011

%Y Cf. A001824, A002554.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_

%E More terms from _Ruperto Corso_, Dec 15 2011