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 A335338 P_5(2n+1), the Legendre polynomial of order 5 at 2n+1. 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 6 10:50 EDT 2023. Contains 363142 sequences. (Running on oeis4.)