A017494 a(n) = (11*n + 8)^10.

1073741824, 6131066257801, 590490000000000, 13422659310152401, 144555105949057024, 984930291881790849, 4923990397355877376, 19687440434072265625, 66483263599150104576, 196715135728956532249, 523383555379856794624, 1276136419117121619201, 2892546549760000000000

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 (11,-55,165,-330,462,-462,330,-165,55,-11,1).

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), A017492 (m=8), A017493 (m=9), this sequence (m=10), A017495 (m=11), A017496 (m=12).

Programs

GAP

List([0..20], n-> (11*n+8)^10); # G. C. Greubel, Sep 22 2019

Magma

[(11*n+8)^10: n in [0..20]]; // G. C. Greubel, Sep 22 2019

Maple

seq((11*n+8)^10, n=0..20); # G. C. Greubel, Sep 22 2019

Mathematica

(11*Range[21] -3)^10 (* G. C. Greubel, Sep 22 2019 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{1073741824,6131066257801,590490000000000,13422659310152401,144555105949057024,984930291881790849,4923990397355877376,19687440434072265625,66483263599150104576,196715135728956532249,523383555379856794624},20] (* Harvey P. Dale, May 08 2022 *)

PARI

vector(20, n, (11*n-3)^10) \\ G. C. Greubel, Sep 22 2019

Sage

[(11*n+8)^10 for n in (0..20)] # G. C. Greubel, Sep 22 2019

Formula

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

G.f.: (1073741824 [phone]*x [phone]*x^2 +7264300786930496 *x^3 +28371531939645368*x^4 +37662294296897282*x^5 +17578871136786818* x^6 +2623025688296696*x^7 [phone]*x^8 [phone]*x^9 +59049* x^10)/(1-x)^11.

E.g.f.: (1073741824 [phone]*x [phone]*x^2 +1944930239197330*x^3 +3932620229881585*x^4 +3254225912463141*x^5 + 1282086963575187*x^6 [phone]*x^7 [phone]*x^8 + 1355819922325*x^9 [phone]*x^10)*exp(x). (End)

Extensions

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