A001797 Coefficients of Legendre polynomials. (Formerly M2118 N0836)

2, 20, 110, 2600, 16150, 208012, 1376550, 74437200, 511755750, 7134913500, 50315410002, 1433226830360, 10292051290430, 148889972762300, 1083802983548950, 126935005433253024, 933787075442258310, 13799767368300523260

Offset

1,1

Comments

Coefficient of Legendre_2(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.

Maple

a:=n->(10*n/((2*n+1)*(2*n+3)))*numer(binomial(4*n, 2*n)/2^(4*n)); # Sean A. Irvine, Nov 28 2012

Mathematica

A001797[n_]:= With[{B=Binomial}, 20*B[n+1, 2]*Numerator[B[4*n, 2*n]/2^(4*n)]/( 3*B[2*n+3, 3])];
Table[A001797[n], {n, 30}] (* G. C. Greubel, Apr 23 2025 *)

Prog

(Magma)
B:= Binomial;
A001797:= func< n | 20*B(n+1, 2)*Numerator(B(4*n, 2*n)/2^(4*n))/(3*B(2*n+3, 3)) >;
[A001797(n): n in [1..30]]; // G. C. Greubel, Apr 23 2025
(SageMath)
b=binomial
def A001797(n): return 20*b(n+1, 2)*numerator(b(4*n, 2*n)/2^(4*n))/(3*b(2*n+3, 3))
print([A001797(n) for n in range(1, 31)]) # G. C. Greubel, Apr 23 2025

Crossrefs

Cf. A001796.

Sequence in context: A073077 A069537 A282818 * A084894 A203238 A061004

Adjacent sequences: A001794 A001795 A001796 * A001798 A001799 A001800

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Nov 28 2012

Status

approved