A017457 a(n) = (11*n + 5)^9.

1953125, 68719476736, 7625597484987, 165216101262848, 1628413597910449, 10077696000000000, 45848500718449031, 167619550409708032, 520411082988487293, 1423311812421484544, 3517876291919921875

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• 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+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), this sequence (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

Programs

GAP

List([0..20], n-> (11*n+5)^9); # G. C. Greubel, Sep 19 2019

Magma

[(11*n+5)^9: n in [0..20]]; // Vincenzo Librandi, Sep 03 2011

Maple

seq((11*n+5)^9, n=0..20); # G. C. Greubel, Sep 19 2019

Mathematica

(11Range[0,20]+5)^9 (* or *) LinearRecurrence[ {10,-45,120,-210,252,-210, 120,-45,10,-1}, {1953125, 68719476736, 7625597484987, 165216101262848, 1628413597910449, 10077696000000000, 45848500718449031, 167619550409708032, 520411082988487293, 1423311812421484544}, 20] (* Harvey P. Dale, Apr 08 2019 *)

PARI

vector(20, n, (11*n-6)^9) \\ G. C. Greubel, Sep 19 2019

Sage

[(11*n+5)^9 for n in (0..20)] # G. C. Greubel, Sep 19 2019

Formula

From G. C. Greubel, Sep 19 2019: (Start)

G.f.: (1953125 [phone]*x [phone]*x^2 [phone]*x^3 [phone]*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 [phone]*x^8 [phone]*x^9)/(1-x)^10.

E.g.f.: (1953125 [phone]*x [phone]*x^2 [phone]*x^3 [phone]*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 [phone]*x^8 [phone]*x^9)*exp(x). (End)