OFFSET
0,2
LINKS
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
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 02 2020
STATUS
approved