A168116 a(n) = n*(n^8+1)/2.

0, 1, 257, 9843, 131074, 976565, 5038851, 20176807, 67108868, 193710249, 500000005, 1178973851, 2579890182, 5302249693, 10330523399, 19221679695, 34359738376, 59293938257, 99179645193, 161343848899, 256000000010, 397140023301, 603634608907

Offset

0,3

Links

Kelvin Voskuijl, Table of n, a(n) for n = 0..10000 (terms 0..1000 by G. C. Greubel)

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

Formula

G.f.: x*(1 + 247*x + 7318*x^2 + 44089*x^3 + 78130*x^4 + 44089*x^5 + 7318*x^6 + 247*x^7 + x^8)/(1 - x)^10. - R. J. Mathar, Oct 13 2011

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10). - Wesley Ivan Hurt, Jun 26 2022

Mathematica

Table[n*(n^8 + 1)/2, {n, 0, 50}] (* G. C. Greubel, Jul 13 2016 *)
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 257, 9843, 131074, 976565, 5038851, 20176807, 67108868, 193710249}, 30] (* Harvey P. Dale, Jul 12 2025 *)

Prog

(Magma) [n*(n^8+1)/2: n in [0..25]]; // Vincenzo Librandi, Jul 14 2016
(PARI) a(n)=(n^9+n)/2 \\ Charles R Greathouse IV, May 26 2026

Crossrefs

Sequence in context: A023877 A301552 A279641 * A086022 A125649 A219549

Adjacent sequences: A168113 A168114 A168115 * A168117 A168118 A168119

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 2009

Status

approved