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A002462
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Coefficients of Legendre polynomials.
(Formerly M4633 N1979)
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0
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1, 9, 50, 1225, 7938, 106722, 736164, 41409225, 295488050, 4266847442, 31102144164, 914057459042, 6760780022500, 100583849722500, 751920156592200, 90324408810638025, 680714748752836050, 10294760089163261250, 78080479568224402500, 2375208188465386324050
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Appears to divide A002894(n+1). - R. Stephan, Aug 23 2004
Constant term of the Legendre polynomials of even order when they are expressed in terms of the cosine function (see 22.3.13 from Abramowitz & Stegun) with the denominators factored out. Also, constant term of the Tisserand functions of even order for the planar case with the denominators factored out (see Table 1 from Laskar & Boué's paper). - Ruperto Corso, Dec 08 2011
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REFERENCES
| A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 362.
G. Pr\'{e}vost, Tables de Fonctions Sph\'{e}riques. Gauthier-Villars, Paris, 1933, pp. 156-157.
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).
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LINKS
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 776.
J. Laskar and G. Boué, Explicit expansion of the three-body disturbing function for arbitrary eccentricities and inclinations, A&A 522, A60 (November 2010).
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MAPLE
| f:=(n, q)->binomial(2*(n-q), (n-q))*binomial(2*q, q)/(4^n):seq(f(2*m, m)*lcm(seq(denom(2*f(2*m, i)), i=0..m-1), denom(f(2*m, m))), m=1..25); # Ruperto Corso, Dec 08 2011
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CROSSREFS
| Sequence in context: A007681 A115366 A188210 * A034814 A034816 A140381
Adjacent sequences: A002459 A002460 A002461 * A002463 A002464 A002465
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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
| Sequence extended by Ruperto Corso, Dec 08 2011
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