The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A002553 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A002553

Coefficients for numerical differentiation.
(history; published version)

#31 by N. J. A. Sloane at Sat Jul 18 13:17:00 EDT 2015

STATUS

editing

approved

#30 by N. J. A. Sloane at Sat Jul 18 13:16:57 EDT 2015

LINKS

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]

STATUS

approved

editing

#29 by Ralf Stephan at Wed Apr 09 03:59:13 EDT 2014

STATUS

proposed

approved

#28 by Jon E. Schoenfield at Sun Mar 30 11:56:40 EDT 2014

STATUS

editing

proposed

Discussion

Wed Apr 09

03:59

Ralf Stephan: Good to see another conjecture gone.

#27 by Jon E. Schoenfield at Sun Mar 30 11:56:38 EDT 2014

FORMULA

a(n) is the denominator of(-1)^(n-1)*Cn-1{1^2..(2n-1)^2}/((2n+1)!*2^(2n)), 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. - By __Sean A. Irvine_ , after _Ruperto Corso, _, Mar 29, 2014

MAPLE

with(combinat): a:=n->add(mul(k, k=j), j=choose([seq((2*i-1)^2, i=1..n)], n))*(-1)^(n-1)/(2^(2*n)*(2*n+1)!):seq(a(n), n=0..20); # By __Sean A. Irvine_ , after _Ruperto Corso_

STATUS

proposed

editing

#26 by Joerg Arndt at Sun Mar 30 06:05:57 EDT 2014

STATUS

editing

proposed

#25 by Joerg Arndt at Sun Mar 30 06:05:51 EDT 2014

COMMENTS

Numbers so far divide A052469(2n+1). - Ralf Stephan, Aug 24 2004

STATUS

proposed

editing

#24 by Michel Marcus at Sun Mar 30 04:34:45 EDT 2014

STATUS

editing

proposed

#23 by Michel Marcus at Sun Mar 30 04:33:47 EDT 2014

REFERENCES

T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. 2, Engelmann, Leipzig, 1880, p. 23.

STATUS

proposed

editing

Discussion

Sun Mar 30

04:34

Michel Marcus: done

#22 by Sean A. Irvine at Sun Mar 30 02:39:57 EDT 2014

STATUS

editing

proposed