A017508 a(n) = (11*n + 9)^12.

282429536481, 4096000000000000, 787662783788549761, 30129469486639681536, 491258904256726154641, 4722366482869645213696, 31676352024078369140625, 163674647745587512938496, 693842360995438000295041, 2518170116818978404827136

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 (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 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), A017506 (m=10), A017607 (m=11), this sequence (m=12).

Programs

GAP

List([0..20], n-> (11*n+9)^12); # G. C. Greubel, Oct 29 2019

Magma

[(11*n+9)^12: n in [0..20]]; // G. C. Greubel, Oct 29 2019

Maple

seq((11*n+9)^12, n=0..0); # G. C. Greubel, Oct 28 2019

Mathematica

(11*Range[20] -2)^12 (* G. C. Greubel, Oct 29 2019 *)

Maxima

makelist((11*n+9)^12, n,0,30); /* Martin Ettl, Oct 21 2012 */

PARI

vector(21, n, (11*n-2)^12) \\ G. C. Greubel, Oct 29 2019

Sage

[(11*n+9)^12 for n in (0..20)] # G. C. Greubel, Oct 29 2019

Formula

From G. C. Greubel, Oct 29 2019: (Start)

G.f.: (282429536481 +4092328416025747*x +734436813292395279*x^2 + 20209260522541101077*x^3 +159842244003035759946*x^4 + 463756067839761680478*x^5 +544661828676570185790*x^6 +

262487410539784705770*x^7 +48674358916489218693*x^8 + 2906273242026287199*x^9 +36217472329783811*x^10 [phone]*x^11 + 4096*x^12)/(1-x)^13.

E.g.f.: (282429536481 + 4095717570463519*x + 389735533109043121*x^2 + 4629794808807415962*x^3 +15643775803972010981*x^4 +21329254236100801848* x^5 +14055885648635908792*x^6 +4951158185239377540*x^7 + 983467446953859582*x^8 +112116203770421565*x^9 +7184433177655591*x^10 + 237949933289574*x^11 [phone]*x^12)*exp(x). (End)