A017517 a(n) = (11*n + 10)^9.

1000000000, 794280046581, 35184372088832, 502592611936843, 3904305912313344, 20711912837890625, 84590643846578176, 285544154243029527, 833747762130149888, 2171893279442309389, 5159780352000000000

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+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), this sequence (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

Programs

GAP

List([0..20], n-> (11*n+10)^9); # G. C. Greubel, Oct 29 2019

Magma

[(11*n+10)^9: n in [0..20]]; // G. C. Greubel, Oct 29 2019

Maple

seq((11*n+10)^9, n=0..20); # G. C. Greubel, Oct 29 2019

Mathematica

(11*Range[20] -1)^9 (* G. C. Greubel, Oct 29 2019 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1000000000,794280046581,35184372088832,502592611936843,3904305912313344,20711912837890625,84590643846578176,285544154243029527,833747762130149888,2171893279442309389},20] (* Harvey P. Dale, Apr 02 2024 *)

Maxima

makelist((11*n+10)^9,n,0,30); /* Martin Ettl, Oct 21 2012 */

PARI

vector(21, n, (11*n-1)^9) \\ G. C. Greubel, Oct 29 2019

Sage

[(11*n+10)^9 for n in (0..20)] # G. C. Greubel, Oct 29 2019

Formula

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

G.f.: (1000000000 + 784280046581*x + 27286571623022*x^2 + 186371493144668* x^3 + 366572931352634*x^4 + 229943411037290*x^5 + 42937656267554*x^6 + 1749554857988*x^7 + 5159780342*x^8 + x^9)/(1-x)^10.

E.g.f.: (1000000000 + 793280046581*x + 16798405997835*x^2 + 66570222635015* x^3 + 87577732371360*x^4 + 48903633958641*x^5 + 12992922453126*x^6 + 1699710028962*x^7 + 104178416166*x^8 + 2357947691*x^9)*exp(x). (End)