A017505 a(n) = (11*n + 9)^9.

387420489, 512000000000, 26439622160671, 406671383849472, 3299763591802133, 18014398509481984, 75084686279296875, 257327417311663616, 760231058654565217, 1999004627104432128, 4785448563124474679

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Powers of the form (11*n+9)^m: A017497 (m=1), A017498 (m=2), A017499 (m=3), A017500 (m=4), A017501 (m=5), A017502 (m=6), A017503 (m=7), A017504 (m=8), this sequence (m=9), A017506 (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A001017.

Programs

GAP

List([0..20], n-> (11*n+9)^9); # G. C. Greubel, Oct 28 2019

Magma

[(11*n+9)^9: n in [0..20]]; // G. C. Greubel, Oct 28 2019

Maple

seq((11*n+9)^9, n=0..20); # G. C. Greubel, Oct 28 2019

Mathematica

(11*Range[20] -2)^9 (* G. C. Greubel, Oct 28 2019 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{387420489,512000000000,26439622160671,406671383849472,3299763591802133,18014398509481984,75084686279296875,257327417311663616,760231058654565217,1999004627104432128},20] (* Harvey P. Dale, Nov 18 2022 *)

Maxima

makelist((11*n+9)^9, n, 0, 30); /* Martin Ettl, Oct 21 2012 */

PARI

vector(21, n, (11*n-2)^9) \\ G. C. Greubel, Oct 28 2019

Sage

[(11*n+9)^9 for n in (0..20)] # G. C. Greubel, Oct 28 2019

Formula

From G. C. Greubel, Oct 28 2019: (Start)

G.f.: (387420489 + 508125795110*x + 21337056082676*x^2 + 165268671784082*x^3 + 361474108840298*x^4 + 251642575443146*x^5 + 52874765679980*x^6 + 2535762569534*x^7 + 10604494253*x^8 + 512*x^9)/(1-x)^10.

E.g.f.: (387420489 + 511612579511*x + 12708004790580*x^2 + 54814688324495* x^3 + 76236174032865*x^4 + 44337148166157*x^5 + 12159505753164*x^6 + 1632362365986*x^7 + 102249186237*x^8 + 2357947691*x^9)*exp(x). (End)