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%I A002555 M5177 N2249 #32 Feb 27 2019 14:03:01
%S A002555 1,24,5760,322560,51609600,13624934400,19837904486400,2116043145216,
%T A002555 20720294477955072,15747423803245854720,131978409017679544320,
%U A002555 72852081777759108464640,151532330097738945606451200,2828603495157793651320422400,19687080326298243813190139904000
%N A002555 Denominators of coefficients for numerical differentiation.
%D A002555 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002555 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002555 Ruperto Corso, <a href="/A002555/b002555.txt">Table of n, a(n) for n = 1..387</a>
%H A002555 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 A002555 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 A002555 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 A002555 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 A002555 a(n) = denominator(A001824(n-1)*(-1)^(n-1)/(2^(2*n-3)*(2*n)!)). - _Sean A. Irvine_, Mar 29 2014
%p A002555 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 A002555 Cf. A001824, A002554.
%K A002555 nonn,frac
%O A002555 1,2
%A A002555 _N. J. A. Sloane_
%E A002555 More terms from _Ruperto Corso_, Dec 15 2011

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