A017444 a(n) = (11*n + 4)^8.

65536, 2562890625, 208827064576, 3512479453921, 28179280429056, 146830437604321, 576480100000000, 1853020188851841, 5132188731375616, 12667700813876161, 28525864220672256, 59604644775390625, 117033789351264256, 218041257467152161, 388379855336079616

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• 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+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), this sequence (m=8), A017445 (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

Programs

GAP

List([0..20], n-> (11*n+4)^8); # G. C. Greubel, Sep 18 2019

Magma

[(11*n+4)^8: n in [0..20]]; // G. C. Greubel, Sep 18 2019

Maple

seq((11*n+4)^8, n=0..20); # G. C. Greubel, Sep 18 2019

Mathematica

(11*Range[0,20]+4)^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36, -9,1}, {65536,2562890625,208827064576,3512479453921, 28179280429056, 146830437604321,576480100000000,1853020188851841,5132188731375616}, 20] (* Harvey P. Dale, Sep 21 2016 *)

PARI

vector(20, n, (11*n-7)^8) \\ G. C. Greubel, Sep 18 2019

Sage

[(11*n+4)^8 for n in (0..20)] # G. C. Greubel, Sep 18 2019

Formula

From G. C. Greubel, Sep 18 2019: (Start)

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

E.g.f.: (65536 [phone]*x [phone]*x^2 [phone]*x^3 [phone]*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 [phone]*x^8)*exp(x). (End)

Extensions

Terms a(12) onward added by G. C. Greubel, Sep 18 2019