A170797 a(n) = n^10*(n^5+1)/2.

0, 1, 16896, 7203978, 537395200, 15263671875, 235122725376, 2373921992596, 17592722915328, 102947309439525, 500005000000000, 2088637053420126, 7703541745975296, 25593015436291303, 77784192406233600

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Crossrefs

Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), A170796 (m=4), this sequence (m=5), A170798 (m=6), A170799 (m=7), A170800 (m=8), A170801 (m=9), A170802 (m=10).

Programs

GAP

List([0..20], n-> n^10*(n^5 +1)/2); # G. C. Greubel, Oct 11 2019

Magma

[n^10*(n^5+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 26 2011

Maple

A170797:=n->n^10*(n^5+1)/2: seq(A170797(n), n=0..20); # Wesley Ivan Hurt, Aug 10 2016

Mathematica

Table[n^10*(n^5 + 1)/2, {n, 0, 15}] (* Wesley Ivan Hurt, Aug 10 2016 *)

PARI

vector(21, m, (m-1)^10*((m-1)^5 + 1)/2) \\ G. C. Greubel, Oct 11 2019

Sage

[n^10*(n^5 +1)/2 for n in (0..20)] # G. C. Greubel, Oct 11 2019

Formula

G.f.: x*(15872*x^13 +6890977*x^12 [phone]*x^11 [phone]*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 +6933762*x^2 +16880*x +1) / (x-1)^16. - Colin Barker, Nov 01 2014

a(n) = 16*a(n-1) - 120*a(n-2) + 560*a(n-3) - 1820*a(n-4) + 4368*a(n-5) - 8008*a(n-6) + 11440*a(n-7) - 12870*a(n-8) + 11440*a(n-9) - 8008*a(n-10) + 4368*a(n-11) - 1820*a(n-12) + 560*a(n-13) - 120*a(n-14) + 16*a(n-15) - a(n-16) for n > 15. - Wesley Ivan Hurt, Aug 10 2016

E.g.f.: x*(2 +16894*x +2384431*x^2 [phone]*x^3 [phone]*x^4 + 420716100*x^5 [phone]*x^6 [phone]*x^7 [phone]*x^8 [phone]*x^9 +1479478*x^10 +106470*x^11 +4550*x^12 +105*x^13 +x^14)*exp(x)/2. - G. C. Greubel, Oct 11 2019