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A002554
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Numerators of coefficients for numerical differentiation.
(Formerly M4034 N1676)
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2
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1, -5, 259, -3229, 117469, -7156487, 2430898831, -60997921, 141433003757, -25587296781661, 51270597630767, -6791120985104747, 3400039831130408821, -15317460638921852507, 25789165074168004597399, -1550286106708510672406629, 24823277118070193095631689
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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).
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).
T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. 2, Engelmann, Leipzig, 1880, p. 23.
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LINKS
| Ruperto Corso, Table of n, a(n) for n = 1..387
T. R. Van Oppolzer, Lehrbuch zur Bahnbestimmung der Kometen und Planeten, Vol. 2, Engelmann, Leipzig, 1880, p. 23.
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FORMULA
| a(n) is the numerator of (-1)^(n-1)*Cn-1{1^2..(2n-1)^2}/((2n)!*2^(2n-3)), where Cn{1^2..(2n+1)^2} equals 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
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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(numer(a(n)), n=1..20); # Ruperto Corso, Dec 15 2011
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CROSSREFS
| Cf. A002555.
Sequence in context: A201606 A139000 A061959 * A003383 A195575 A195553
Adjacent sequences: A002551 A002552 A002553 * A002555 A002556 A002557
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Corrected and extended by Ruperto Corso (rupertocorsoto(AT)gmail.com), Dec 15 2011
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