This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A002462 M4633 N1979 #46 Mar 31 2025 11:55:38
%S A002462 1,1,9,50,1225,7938,106722,736164,41409225,295488050,4266847442,
%T A002462 31102144164,914057459042,6760780022500,100583849722500,
%U A002462 751920156592200,90324408810638025,680714748752836050,10294760089163261250,78080479568224402500,2375208188465386324050
%N A002462 Coefficients of Legendre polynomials.
%C A002462 Appears to divide A002894(n+1). - _Ralf Stephan_, Aug 23 2004
%C A002462 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). Cf. A002463. - _Ruperto Corso_, Dec 08 2011
%D A002462 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 A002462 G. Prévost, Tables de Fonctions Sphériques. Gauthier-Villars, Paris, 1933, pp. 156-157.
%D A002462 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002462 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002462 M. Abramowitz and I. A. Stegun, eds., <a href="https://personal.math.ubc.ca/~cbm/aands/page_776.htm">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 776.
%H A002462 J. Laskar and G. Boué, <a href="https://arxiv.org/abs/1008.2947">Explicit expansion of the three-body disturbing function for arbitrary eccentricities and inclinations</a>, arXiv:1008.2947 [astro-ph.IM], 2010; A&A 522, A60 (November 2010).
%F A002462 This is binomial(2*n,n)^2/2^(4*n) multiplied by some power of 2, but the exact power of 2 needed is a bit hard to describe precisely. No doubt Prévost or Fletcher et al., where I saw this sequence 40 years ago, will have the answer. - _N. J. A. Sloane_, Jun 01 2013
%p A002462 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=0..25); # _Ruperto Corso_, Dec 08 2011
%t A002462 f[n_, q_] := Binomial[2(n-q), n-q] Binomial[2q, q]/4^n;
%t A002462 a[m_] := f[2m, m] LCM @@ Append[Table[Denominator[2f[2m, i]], {i, 0, m-1}], Denominator[f[2m, m]]];
%t A002462 Table[a[m], {m, 0, 25}] (* _Jean-François Alcover_, Jan 20 2019, after _Ruperto Corso_ *)
%K A002462 nonn
%O A002462 0,3
%A A002462 _N. J. A. Sloane_
%E A002462 Sequence extended by _Ruperto Corso_, Dec 08 2011