A017471 - OEIS

%I #15 Sep 08 2022 08:44:42

%S 362797056,34271896307633,8293509467471872,317475837322472439,

%T 4882812500000000000,43513917611435838661,269561249468963094528,

%U 1287831418538085836267,5062982072492057196544,17103393581163134765625

%N a(n) = (11*n + 6)^11.

%H Vincenzo Librandi, <a href="/A017471/b017471.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

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

%F G.f.: (362797056 +34267542742961*x +7882270656385972*x^2 + 220215589053761433*x^3 +1612934439380337744*x^4 +4065965093212217778*x^5 +3893323100536505064*x^6 +1409984186533172778*x^7 +173024396961630192* x^8 +5347957556678781*x^9 +17591600106916*x^10 +48828125 x^11)/(1-x)^12.

%F E.g.f.: (362797056 +34271533510577*x +4112483018826831*x^2 + 48783020707697111*x^3 +152605546678854500*x^4 +184932081242538212*x^5 + 104853627173466171*x^6 +30701237124182097*x^7 +4849119426541500*x^8 + 411237867048855*x^9 +17404011907271*x^10 +285311670611*x^11)*exp(x). (End)

%p seq((11*n+6)^11, n=0..20); # _G. C. Greubel_, Sep 19 2019

%t (11*Range[20] -5)^11 (* _G. C. Greubel_, Sep 19 2019 *)

%o (Magma) [(11*n+6)^11: n in [0..10]]; // _Vincenzo Librandi_, Sep 04 2011

%o (PARI) vector(20, n, (11*n-5)^11) \\ _G. C. Greubel_, Sep 19 2019

%o (Sage) [(11*n+6)^11 for n in (0..20)] # _G. C. Greubel_, Sep 19 2019

%o (GAP) List([0..20], n-> (11*n+6)^11); # _G. C. Greubel_, Sep 19 2019

%Y Powers of the form (11*n+6)^m: A017461 (m=1), A017462 (m=2), A017463 (m=3), A017464 (m=4), A017465 (m=5), A017466 (m=6), A017467 (m=7), A017468 (m=8), A017469 (m=9), A017470 (m=10), this sequence (m=11), A017472 (m=12).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_