A017492 a(n) = (11*n + 8)^8.

16777216, 16983563041, 656100000000, 7984925229121, 53459728531456, 248155780267521, 899194740203776, 2724905250390625, 7213895789838336, 17181861798319201, 37588592026706176, 76686282021340161, 147578905600000000, 270281038127131201, 474373168346071296

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+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), A017491 (m=7), this sequence (m=8), A017493 (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

Programs

GAP

List([0..20], n-> (11*n+8)^8); # G. C. Greubel, Sep 22 2019

Magma

[(11*n+8)^8: n in [0..20]]; // G. C. Greubel, Sep 22 2019

Maple

seq((11*n+8)^8, n=0..20); # G. C. Greubel, Sep 22 2019

Mathematica

(11*Range[21] -3)^8 (* G. C. Greubel, Sep 22 2019 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{16777216,16983563041,656100000000,7984925229121,53459728531456,248155780267521,899194740203776,2724905250390625,7213895789838336},20] (* Harvey P. Dale, Jul 02 2024 *)

PARI

vector(20, n, (11*n-3)^8) \\ G. C. Greubel, Sep 22 2019

Sage

[(11*n+8)^8 for n in (0..20)] # G. C. Greubel, Sep 22 2019

Formula

From G. C. Greubel, Sep 22 2019: (Start)

G.f.: (16777216 [phone]*x [phone]*x^2 [phone]*x^3 + 3790496103139*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 + 6561*x^8)/(1-x)^9.

E.g.f.: (16777216 [phone]*x [phone]*x^2 [phone]*x^3 + 1057862922501*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 + 214358881*x^8)*exp(x). (End)

Extensions

More terms added by G. C. Greubel, Sep 22 2019