A335338 P_5(2n+1), the Legendre polynomial of order 5 at 2n+1.

1, 1683, 23525, 129367, 458649, 1256651, 2904733, 5950575, 11138417, 19439299, 32081301, 50579783, 76767625, 112825467, 161311949, 225193951, 307876833, 413234675, 545640517, 709996599, 911764601, 1156995883, 1452361725, 1805183567, 2223463249, 2715913251, 3291986933

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Eric Weisstein's World of Mathematics, Legendre Polynomial.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = A160737(2*n+1)/4.

a(n) = 252*n^5 + 630*n^4 + 560*n^3 + 210*n^2 + 30*n + 1 = (2*n + 1) * (126*n^4 + 252*n^3 + 154*n^2 + 28*n + 1).

G.f.: (1+x)*(1+1676*x+11766*x^2+1676*x^3+x^4)/(1-x)^6.

Mathematica

a[n_] := LegendreP[5, 2*n + 1]; Array[a, 27, 0] (* Amiram Eldar, May 03 2021 *)

Prog

(PARI) a(n) = pollegendre(5, 2*n+1)
(PARI) a(n) = 252*n^5+630*n^4+560*n^3+210*n^2+30*n+1
(PARI) N=40; x='x+O('x^N); Vec((1+x)*(1+1676*x+11766*x^2+1676*x^3+x^4)/(1-x)^6)

Crossrefs

Row 5 of A335333.

Cf. A160737.

Sequence in context: A031719 A206671 A205515 * A263061 A281062 A020241

Adjacent sequences: A335335 A335336 A335337 * A335339 A335340 A335341

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 02 2020

Status

approved