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A002463 Coefficients of Legendre polynomials.

%I A002463 M3124 N1267 #41 Jun 25 2025 14:30:51
%S A002463 1,3,30,175,4410,29106,396396,2760615,156434850,1122854590,
%T A002463 16291599324,119224885962,3515605611700,26077294372500,
%U A002463 388924218927000,2913690606794775,350671234206006450,2647224022927695750,40095381399899017500,304513870316075169750
%N A002463 Coefficients of Legendre polynomials.
%C A002463 Apparently, a(n) divides A000894(n). - _Ralf Stephan_, Aug 05 2004
%C A002463 Coefficients of cos(x) term of the Tisserand functions of odd order for the planar case with the denominators factored out (see Table 1 from Laskar & Boué's paper) (cf A002462). - _Michel Marcus_, May 29 2013
%C A002463 Also cos(x) term of the Legendre polynomials of odd order when they are expressed in terms of the cosine function (see 22.3.13 from Abramowitz & Stegun) with the denominators factored out. - _Michel Marcus_, May 29 2013
%D A002463 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.
%D A002463 G. Prévost, Tables de Fonctions Sphériques. Gauthier-Villars, Paris, 1933, pp. 156-157.
%D A002463 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002463 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%o A002463 (PARI) lista(nn) = {forstep (n=1, nn, 2, lcmc = 1; for (m=0, n\2, lcmc = lcm(lcmc, denominator(binomial(2*n-2*m, n-m) * binomial(2*m, m)/4^n));); m = n\2; print1(lcmc*binomial(2*n-2*m, n-m) * binomial(2*m, m)/4^n, ", "););} \\ _Michel Marcus_, May 29 2013
%o A002463 (Python)
%o A002463 from sympy import binomial as C, lcm
%o A002463 def a_list(nn):
%o A002463     l = []
%o A002463     for n in range(1, nn + 1, 2):
%o A002463         lcmc = 1
%o A002463         for m in range(n//2 + 1):
%o A002463             lcmc = lcm(lcmc, (C(2*n - 2*m, n - m)*C(2*m, m)/4**n).denominator)
%o A002463         m = n//2
%o A002463         l.append(lcmc*C(2*n - 2*m, n - m)*C(2*m, m)//4**n)
%o A002463     return l # _Indranil Ghosh_, Jul 02 2017, after PARI code by _Michel Marcus_
%K A002463 nonn
%O A002463 1,2
%A A002463 _N. J. A. Sloane_
%E A002463 More terms from _Michel Marcus_, May 29 2013