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a(n) = (11*n + 4)^9.
12

%I #11 Sep 08 2022 08:44:42

%S 262144,38443359375,5429503678976,129961739795077,1352605460594688,

%T 8662995818654939,40353607000000000,150094635296999121,

%U 472161363286556672,1304773183829244583,3251948521156637184

%N a(n) = (11*n + 4)^9.

%H G. C. Greubel, <a href="/A017445/b017445.txt">Table of n, a(n) for n = 0..1000</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 18 2019: (Start)

%F G.f.: (262144 +38440737935*x +5045081881706*x^2 +77396622719912*x^3 +292702580123078*x^4 +341752101417866*x^5 +125993865875030*x^6 +12525368984504*x^7 +197955754298*x^8 +40353607*x^9)/(1-x)^10.

%F E.g.f.: (262144 +38443097231*x +2676308611185*x^2 +18964759762355*x^3 +36049239596370*x^4 +26212359111477*x^5 +8537070967194*x^6 +1316670195786*x^7 +92603036592*x^8 +2357947691*x^9)*exp(x). (End)

%p seq((11*n+4)^9, n=0..20); # _G. C. Greubel_, Sep 18 2019

%t (11*Range[20] -7)^9 (* _G. C. Greubel_, Sep 18 2019 *)

%o (PARI) vector(20, n, (11*n-7)^9) \\ _G. C. Greubel_, Sep 18 2019

%o (Magma) [(11*n+4)^9: n in [0..20]]; // _G. C. Greubel_, Sep 18 2019

%o (Sage) [(11*n+4)^9 for n in (0..20)] # _G. C. Greubel_, Sep 18 2019

%o (GAP) List([0..20], n-> (11*n+4)^9); # _G. C. Greubel_, Sep 18 2019

%Y Powers of the form (11*n+4)^m: A017437 (m=1), A017438 (m=2), A017439 (m=3), A017440 (m=4), A017441 (m=5), A017442 (m=6), A017443 (m=7), A017444 (m=8), this sequence (m=9), A017446 (m=10), A017447 (m=11), A017448 (m=12).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_