A160864 64*P_9(n), 64 times the Legendre polynomial of order 9 at n.

0, 64, 1734443, 93604032, 1391396086, 10892513600, 57713977089, 234800671168, 789011921132, 2293521500736, 5949698591575, 14081075036864, 30899647458018, 63644611431232, 124215678953261, 231447389860800, 414197292706264, 715449540834368, 1197666325048707

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

From Colin Barker, Mar 31 2018: (Start)

G.f.: x*(64 + 1733803*x + 76262482*x^2 + 533398021*x^3 + 982614460*x^4 + 533398021*x^5 + 76262482*x^6 + 1733803*x^7 + 64*x^8) / (1 - x)^10.

a(n) = n*(315 - 4620*n^2 + 18018*n^4 - 25740*n^6 + 12155*n^8) / 2.

(End)

Mathematica

Table[64*LegendreP[9, n], {n, 0, 50}] (* G. C. Greubel, Apr 30 2018 *)

Prog

(PARI) a(n)=pollegendre(9, n)<<6 \\ Charles R Greathouse IV, Oct 26 2011
(PARI) concat(0, Vec(x*(64 + 1733803*x + 76262482*x^2 + 533398021*x^3 + 982614460*x^4 + 533398021*x^5 + 76262482*x^6 + 1733803*x^7 + 64*x^8) / (1 - x)^10 + O(x^20))) \\ Colin Barker, Mar 31 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(64 + 1733803*x + 76262482*x^2 + 533398021*x^3 + 982614460*x^4 + 533398021*x^5 + 76262482*x^6 + 1733803*x^7 + 64*x^8) / (1 - x)^10)); // G. C. Greubel, Apr 30 2018

Crossrefs

Sequence in context: A232722 A017094 A350558 * A017190 A329236 A013847

Adjacent sequences: A160861 A160862 A160863 * A160865 A160866 A160867

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 19 2009

Status

approved