A170796 a(n) = n^10*(n^4 + 1)/2.

0, 1, 8704, 2421009, 134742016, 3056640625, 39212315136, 339252774049, 2199560126464, 11440139619681, 50005000000000, 189887885503921, 641990190956544, 1968757122095569, 5556148040106496, 14596751337890625

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 (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Crossrefs

Sequences of the form n^10*(n^m + 1)/2: A170793 (m=1), A170794 (m=2), A170795 (m=3), this sequence (m=4), A170797 (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^4 +1)/2); # G. C. Greubel, Oct 11 2019

Magma

[n^10*(n^4+1)/2: n in [0..20]]; // Vincenzo Librandi, Aug 26 2011

Maple

seq(n^10*(n^4 +1)/2, n=0..20); # G. C. Greubel, Oct 11 2019

Mathematica

Table[n^10*(n^4 +1)/2, {n,0,20}] (* G. C. Greubel, Oct 11 2019 *)

PARI

vector(21, m, (m-1)^10*((m-1)^4 + 1)/2) \\ G. C. Greubel, Oct 11 2019

Sage

[n^10*(n^4 +1)/2 for n in (0..20)] # G. C. Greubel, Oct 11 2019

Formula

From G. C. Greubel, Oct 11 2019: (Start)

G.f.: x*(1 +8689*x +2290554*x^2 [phone]*x^3 [phone]*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 [phone]*x^8 [phone]*x^9 [phone]*x^10 +2290554*x^11 +8689*x^12 +x^13)/(1-x)^15.

E.g.f.: x*(2 +8702*x +798300*x^2 [phone]*x^3 [phone]*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 +5135175*x^8 +752753*x^9 + 66066*x^10 +3367*x^11 +91*x^12 +x^13)*exp(x)/2. (End)