A170786 a(n) = n^9*(n^4 + 1)/2.

0, 1, 4352, 807003, 33685504, 611328125, 6535385856, 48464682007, 274945015808, 1271126624409, 5000500000000, 17262535045811, 53499182579712, 151442855545813, 396867717150464, 973116755859375, 2251834173423616, 4952348310391217, 10411581612480768

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91,14, -1).

Formula

From Colin Barker, Dec 06 2017: (Start)

G.f.: x*(1 + 4338*x + 746166*x^2 + 22783130*x^3 + 211585215*x^4 + 752778228*x^5 + 1137716244*x^6 + 752778228*x^7 + 211585215*x^8 + 22783130*x^9 + 746166*x^10 + 4338*x^11 + x^12) / (1 - x)^14.

a(n) = 14*a(n-1) - 91*a(n-2) + 364*a(n-3) - 1001*a(n-4) + 2002*a(n-5) - 3003*a(n-6) + 3432*a(n-7) - 3003*a(n-8) + 2002*a(n-9) - 1001*a(n-10) + 364*a(n-11) - 91*a(n-12) - 14*a(n-13) + a(n-14) for n>13.

(End)

Mathematica

Table[n^9 (n^4+1)/2, {n, 0, 30}] (* or *) LinearRecurrence[{14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1}, {0, 1, 4352, 807003, 33685504, 611328125 , 6535385856, 48464682007, 274945015808, 1271126624409, 5000500000000, 17262535045811, 53499182579712, 151442855545813}, 30] (* Harvey P. Dale, Aug 22 2016 *)

Prog

(Magma) [n^9*(n^4+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 26 2011
(PARI) for(n=0, 30, print1(n^9*(n^4+1)/, ", ")) \\ G. C. Greubel, Dec 06 2017
(PARI) concat(0, Vec(x*(1 + 4338*x + 746166*x^2 + 22783130*x^3 + 211585215*x^4 + 752778228*x^5 + 1137716244*x^6 + 752778228*x^7 + 211585215*x^8 + 22783130*x^9 + 746166*x^10 + 4338*x^11 + x^12) / (1 - x)^14 + O(x^20))) \\ Colin Barker, Dec 06 2017

Crossrefs

Sequence in context: A294985 A252302 A235066 * A223378 A239193 A068292

Adjacent sequences: A170783 A170784 A170785 * A170787 A170788 A170789

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 2009

Status

approved