A017457 - OEIS

%I #18 Sep 08 2022 08:44:42

%S 1953125,68719476736,7625597484987,165216101262848,1628413597910449,

%T 10077696000000000,45848500718449031,167619550409708032,

%U 520411082988487293,1423311812421484544,3517876291919921875

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

%H Vincenzo Librandi, <a href="/A017457/b017457.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F From _G. C. Greubel_, Sep 19 2019: (Start)

%F G.f.: (1953125 +68699945486*x +6938490608252*x^2 +92052268491098*x^3 +311158545054314*x^4 +327643477452290*x^5 +108279046743524*x^6 +9393030684758*x^7 +118487099537*x^8 +10077696*x^9)/(1-x)^10.

%F E.g.f.: (1953125 +68717523611*x +3744080242320*x^2 +23757577547495*x^3 +42209495908965*x^4 +29265638697141*x^5 +9191914318356*x^6 +1377002477202*x^7 +94532266521*x^8 +2357947691*x^9)*exp(x). (End)

%p seq((11*n+5)^9, n=0..20); # _G. C. Greubel_, Sep 19 2019

%t (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 *)

%o (Magma) [(11*n+5)^9: n in [0..20]]; // _Vincenzo Librandi_, Sep 03 2011

%o (PARI) vector(20, n, (11*n-6)^9) \\ _G. C. Greubel_, Sep 19 2019

%o (Sage) [(11*n+5)^9 for n in (0..20)] # _G. C. Greubel_, Sep 19 2019

%o (GAP) List([0..20], n-> (11*n+5)^9); # _G. C. Greubel_, Sep 19 2019

%Y 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).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_