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A002555
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Denominators of coefficients for numerical differentiation.
(Formerly M5177 N2249)
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2
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1, 24, 5760, 322560, 51609600, 13624934400, 19837904486400, 2116043145216, 20720294477955072, 15747423803245854720, 131978409017679544320, 72852081777759108464640, 151532330097738945606451200, 2828603495157793651320422400, 19687080326298243813190139904000
(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 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
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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(denom(a(n)), n=1..20); # Ruperto Corso, Dec 15 2011
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CROSSREFS
| Cf. A002554.
Sequence in context: A100089 A151598 A003787 * A002198 A163576 A145408
Adjacent sequences: A002552 A002553 A002554 * A002556 A002557 A002558
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Ruperto Corso (rupertocorsoto(AT)gmail.com), Dec 15 2011
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