The On-Line Encyclopedia of Integer Sequences (OEIS)

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A002555

Denominators of coefficients for numerical differentiation.
(history; published version)

#32 by Alois P. Heinz at Wed Feb 27 14:03:01 EST 2019

STATUS

proposed

approved

#31 by Michel Marcus at Wed Feb 27 12:01:51 EST 2019

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editing

proposed

#30 by Michel Marcus at Wed Feb 27 12:01:47 EST 2019

LINKS

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.

FORMULA

a(n) = denomdenominator(A001824(n-1)*(-1)^(n-1)/(2^(2*n-3)*(2*n)!)). - Sean A. Irvine, Mar 29 2014

STATUS

approved

editing

#29 by N. J. A. Sloane at Sat Jul 18 13:17:48 EDT 2015

STATUS

editing

approved

#28 by N. J. A. Sloane at Sat Jul 18 13:17:45 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

#27 by Bruno Berselli at Sun Mar 30 01:48:32 EDT 2014

STATUS

proposed

approved

#26 by Michel Marcus at Sun Mar 30 01:43:56 EDT 2014

STATUS

editing

proposed

#25 by Michel Marcus at Sun Mar 30 01:43:46 EDT 2014

REFERENCES

W. G. Bickley and J. C. P. Miller, Numerical differentiation near the limits of a difference table, Phil. Mag., 33 (1942), 1-12 (plus tables).

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

LINKS

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).

STATUS

proposed

editing

Discussion

Sun Mar 30

01:43

Michel Marcus: moved 1 ref to links, removed 1 ref already in links

#24 by Jon E. Schoenfield at Sat Mar 29 22:44:55 EDT 2014

STATUS

editing

proposed

#23 by Jon E. Schoenfield at Sat Mar 29 22:44:53 EDT 2014

FORMULA

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

a(n) = denom(A001824(n-1)*(-1)^(n-1)/(2^(2*n-3)*(2*n)!)). - _Sean A. Irvine, _, 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))*(-1)^(n-1)/(2^(2*n-3)*(2*n)!): seq(denom(a(n)), n=1..20); # _Ruperto Corso, _, Dec 15 2011

STATUS

proposed

editing