A017506 a(n) = (11*n + 9)^10.

3486784401, 10240000000000, 819628286980801, 17080198121677824, 174887470365513049, 1152921504606846976, 5631351470947265625, 22130157888803070976, 73742412689492826049, 215892499727278669824

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+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), A017505 (m=9), this sequence (m=10), A017607 (m=11), A017508 (m=12).

Subsequence of A008454.

Programs

GAP

List([0..20], n-> (11*n+9)^10); # G. C. Greubel, Oct 28 2019

Magma

[(11*n+9)^10: n in [0..20]]; // G. C. Greubel, Oct 28 2019

Maple

seq((11*n+9)^10, n=0..20); # G. C. Greubel, Oct 28 2019

Mathematica

(11*Range[20] -2)^10 (* G. C. Greubel, Oct 28 2019 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{3486784401,10240000000000,819628286980801,17080198121677824,174887470365513049,1152921504606846976,5631351470947265625,22130157888803070976,73742412689492826049,215892499727278669824,569468379011812486801},30] (* Harvey P. Dale, Jul 14 2021 *)

PARI

vector(21, n, (11*n-2)^10) \\ G. C. Greubel, Oct 28 2019

Sage

[(11*n+9)^10 for n in (0..20)] # G. C. Greubel, Oct 28 2019

Formula

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

G.f.: (3486784401 + 10201645371589*x + 707180060122856*x^2 + 8626911645462848*x^3 + 30396397449853370*x^4 + 36709149032258330*x^5 + 15541165896383216*x^6 + 2068692379779224*x^7 + 61886937611357*x^8 + 137858480585*x^9 + 1024*x^10)/(1-x)^11.

E.g.f.: (3486784401 + 10236513215599*x + 399575886882601*x^2 + 2442004962325170*x^3 + 4643478795311290*x^4 + 3676175396995563*x^5 + 1399671561315027*x^6 + 274137726759600*x^7 + 27874157090835*x^8 + 1379399399235*x^9 + 25937424601*x^10)*exp(x). (End)