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A002553 Coefficients for numerical differentiation.
(Formerly M5166 N2243)
0
1, 24, 640, 7168, 294912, 2883584, 54525952, 167772160, 36507222016, 326417514496, 5772436045824, 50577534877696, 1759218604441600, 15199648742375424, 261208778387488768, 2233785415175766016, 101457092405402533888 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
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).
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) [Annotated scanned copy]
T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. 2, Engelmann, Leipzig, 1880, p. 23, (see denominators of numbers named M(1,2k+1)).
FORMULA
a(n) = denom(A001818(n)*(-1)^(n-1)/(2^(2*n)*(2*n+1)!)). - Sean A. Irvine, Mar 29 2014
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. - 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); # Sean A. Irvine, after Ruperto Corso
CROSSREFS
Sequence in context: A182611 A331322 A126153 * A006201 A118051 A208441
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Mar 29 2014
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)