A001802 Coefficients of Legendre polynomials.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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].

Crossrefs

Diagonal 4 of triangle A100258.

Cf. A001796, A011371.

Programs

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

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 *)

PARI

a(n)= - polcoeff(pollegendre(n+6), n)*2^valuation((n\2*2+6)!, 2) \\ Michel Marcus, May 29 2013

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

Formula

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

Extensions

More terms from Michel Marcus, Feb 02 2015