A017480 a(n) = (11*n + 7)^8.

5764801, 11019960576, 500246412961, 6553600000000, 45767944570401, 218340105584896, 806460091894081, 2478758911082496, 6634204312890625, 15938480745308416, 35114532758015841, 72057594037927936, 139353667211683681, 256289062500000000, 451447246258894081

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Powers of the form (11*n+7)^m: A017473 (m=1), A017474 (m=2), A017475 (m=3), A017476 (m=4), A017477 (m=5), A017478 (m=6), A017479 (m=7), this sequence (m=8), A017481 (m=9), A017482 (m=10), A017483 (m=11), A017484 (m=12).

Programs

GAP

List([0..20], n-> (11*n+7)^8); # G. C. Greubel, Sep 19 2019

Magma

[(11*n+7)^8: n in [0..20]]; // Vincenzo Librandi, Sep 04 2011

Maple

seq((11*n+7)^8, n=0..20); # G. C. Greubel, Sep 19 2019

Mathematica

(11*Range[0,20]+7)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36, -9,1}, {5764801,11019960576, 500246412961,6553600000000, 45767944570401, 218340105584896,806460091894081,2478758911082496,6634204312890625}, 20] (* Harvey P. Dale, Mar 30 2016 *)

PARI

vector(20, n, (11*n-4)^8) \\ G. C. Greubel, Sep 19 2019

Sage

[(11*n+7)^8 for n in (0..20)] # G. C. Greubel, Sep 19 2019

Formula

From G. C. Greubel, Sep 19 2019: (Start)

G.f.: (5764801 [phone]*x [phone]*x^2 [phone]*x^3 + 3869465113539*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 + 65536*x^8)/(1-x)^9.

E.g.f.: (5764801 [phone]*x [phone]*x^2 [phone]*x^3 + 937956207111*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 + 214358881*x^8)*exp(x). (End)