A002463 Coefficients of Legendre polynomials. (Formerly M3124 N1267)

1, 3, 30, 175, 4410, 29106, 396396, 2760615, 156434850, 1122854590, 16291599324, 119224885962, 3515605611700, 26077294372500, 388924218927000, 2913690606794775, 350671234206006450, 2647224022927695750, 40095381399899017500, 304513870316075169750

Offset

1,2

Comments

Apparently, a(n) divides A000894(n). - Ralf Stephan, Aug 05 2004

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

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

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. Prévost, Tables de Fonctions Sphériques. 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).

Links

Table of n, a(n) for n=1..20.

Prog

(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
(Python)
from sympy import binomial as C, lcm
def a_list(nn):
    l = []
    for n in range(1, nn + 1, 2):
        lcmc = 1
        for m in range(n//2 + 1):
            lcmc = lcm(lcmc, (C(2*n - 2*m, n - m)*C(2*m, m)/4**n).denominator())
        m = n//2
        l.append(lcmc*C(2*n - 2*m, n - m)*C(2*m, m)//4**n)
    return l # Indranil Ghosh, Jul 02 2017, after PARI code by Michel Marcus

Crossrefs

Sequence in context: A161806 A003689 A127868 * A360645 A344564 A013281

Adjacent sequences: A002460 A002461 A002462 * A002464 A002465 A002466

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Michel Marcus, May 29 2013

Status

approved