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
Links
- Eric Weisstein's World of Mathematics, Legendre Polynomial.
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
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Mathematica
a[n_] := LegendreP[5, 2*n + 1]; Array[a, 27, 0] (* Amiram Eldar, May 03 2021 *)
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PARI
a(n) = pollegendre(5, 2*n+1)
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PARI
a(n) = 252*n^5+630*n^4+560*n^3+210*n^2+30*n+1
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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)
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.