A001802 Coefficients of Legendre polynomials. (Formerly M3980 N1649)

5, 35, 1260, 4620, 30030, 90090, 1021020, 2771340, 14549535, 37182145, 1487285800, 3650610600, 17644617900, 42075627300, 396713057400, 925663800600, 4281195077775, 9821565178425, 178970743251300, 405039050516100, 1822675727322450, 4079321865912150

Offset

0,1

References

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 798.

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

G. C. Greubel, Table of n, a(n) for n = 0..1000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Formula

a(n) = 5*2^(n-4)*binomial(n+5/2, n)*2^A011371(n+6). - G. C. Greubel, Apr 26 2025

Mathematica

A001802[n_]:= 5*4^(n+1)*Binomial[n+5/2, n]/2^DigitCount[n+6, 2, 1];
Table[A001802[n], {n, 0, 30}] (* G. C. Greubel, Apr 26 2025 *)

Prog

(PARI) a(n)= - polcoeff(pollegendre(n+6), n)*2^valuation((n\2*2+6)!, 2) \\ Michel Marcus, May 29 2013
(Magma)
A001802:= func< n | Binomial(n+4, 4)*Catalan(n+3)*2^(Valuation(Factorial(n+6), 2)-n-4) >;
[A001802(n): n in [0..30]]; // G. C. Greubel, Apr 26 2025
(SageMath)
def A001802(n): return 5*2^(n-4)*binomial(n+5/2, n)*2^valuation(factorial(n+6), 2)
print([A001802(n) for n in range(31)]) # G. C. Greubel, Apr 26 2025

Crossrefs

Diagonal 4 of triangle A100258.

Cf. A001796, A011371.

Sequence in context: A058015 A053420 A321605 * A383521 A122590 A057991

Adjacent sequences: A001799 A001800 A001801 * A001803 A001804 A001805

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Michel Marcus, Feb 02 2015

Status

approved