A001797 Coefficients of Legendre polynomials.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A001796.

Programs

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

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 *)

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

Extensions

More terms from Sean A. Irvine, Nov 28 2012