|
%I #24 Oct 21 2022 21:55:34
%S 1,1683,23525,129367,458649,1256651,2904733,5950575,11138417,19439299,
%T 32081301,50579783,76767625,112825467,161311949,225193951,307876833,
%U 413234675,545640517,709996599,911764601,1156995883,1452361725,1805183567,2223463249,2715913251,3291986933
%N P_5(2n+1), the Legendre polynomial of order 5 at 2n+1.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LegendrePolynomial.html">Legendre Polynomial</a>.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = A160737(2*n+1)/4.
%F 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).
%F G.f.: (1+x)*(1+1676*x+11766*x^2+1676*x^3+x^4)/(1-x)^6.
%t a[n_] := LegendreP[5, 2*n + 1]; Array[a, 27, 0] (* _Amiram Eldar_, May 03 2021 *)
%o (PARI) a(n) = pollegendre(5, 2*n+1)
%o (PARI) a(n) = 252*n^5+630*n^4+560*n^3+210*n^2+30*n+1
%o (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)
%Y Row 5 of A335333.
%Y Cf. A160737.
%K nonn,easy
%O 0,2
%A _Seiichi Manyama_, Jun 02 2020
|
