A001798 Coefficients of Legendre polynomials. (Formerly M2149 N0856)

2, 28, 182, 4760, 31654, 428260, 2941470, 163761840, 1152562950, 16381761396, 117402623338, 3390322778024, 24634522766126, 360043025043380, 2644479279859438, 312191499849352032, 2312918756095439814, 34398444513178377492

Offset

1,1

Comments

Coefficient of Legendre_3(x) when x^n is written in term of Legendre polynomials. - Sean A. Irvine, Nov 28 2012

References

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 = 1..830

H. E. Salzer, Coefficients for expressing the first twenty-four powers in terms of the Legendre polynomials, Math. Comp., 3 (1948), 16-18.

Formula

a(n) = (14*n/((2*n+3)*(2*n+5)))*numerator(binomial(4*n+2, 2*n+1)/2^(4*n)). - Sean A. Irvine, Nov 28 2012

Maple

a:=n->(14*n/((2*n+3)*(2*n+5)))*numer(binomial(4*n+2, 2*n+1)/2^(4*n)); # Sean A. Irvine, Nov 28 2012

Mathematica

A001798[n_]:= With[{B=Binomial}, 14*B[n+2, 3]*Numerator[B[4*n+2, 2*n+1]/2^(4*n) ]/B[2*n+5, 4]];
Table[A001798[n], {n, 30}] (* G. C. Greubel, Apr 23 2025 *)

Prog

(Magma)
B:=Binomial;
A001798:= func< n | 14*B(n+2, 3)*Numerator(B(4*n+2, 2*n+1)/2^(4*n))/B(2*n+5, 4) >;
[A001798(n): n in [1..30]]; // G. C. Greubel, Apr 23 2025
(SageMath)
b=binomial
def A001798(n): return 14*b(n+2, 3)*numerator(b(4*n+2, 2*n+1)/2^(4*n) )//b(2*n+5, 4)
print([A001798(n) for n in range(1, 31)]) # G. C. Greubel, Apr 23 2025

Crossrefs

Cf. A001796.

Sequence in context: A006332 A280120 A065340 * A123787 A035601 A281124

Adjacent sequences: A001795 A001796 A001797 * A001799 A001800 A001801

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 28 2012

Status

approved