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a(n) = (11*n + 8)^7.
12

%I #13 Sep 08 2022 08:44:42

%S 2097152,893871739,21870000000,194754273881,1028071702528,

%T 3938980639167,12151280273024,32057708828125,75144747810816,

%U 160578147647843,318547390056832,594467302491009,1054135040000000,1789940649848551,2928229434235008,4637914326451397,7140436495826944

%N a(n) = (11*n + 8)^7.

%H G. C. Greubel, <a href="/A017491/b017491.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F G.f.: (2097152 +877094523*x +14777746344*x^2 +44705242061*x^3 +32487494736*x^4 +5260268829*x^5 +105396008*x^6 +2187*x^7)/(1-x)^8. - _R. J. Mathar_, Jun 24 2009

%F a(0)=2097152, a(1)=893871739, a(2)=21870000000, a(3)=194754273881, a(4)=1028071702528, a(5)=3938980639167, a(6)=12151280273024, a(7)=32057708828125, a(n) = 8*a(n-1) -28*a(n-2) +56*a(n-3) -70*a(n-4) +56*a(n-5) -28*a(n-6) +8*a(n-7) -a(n-8). - _Harvey P. Dale_, Aug 14 2015

%F E.g.f.: (2097152 +891774587*x +10042176837*x^2 +21970631991*x^3 + 15695884050*x^4 +4432767724*x^5 +508438007*x^6 +19487171*x^7)*exp(x). - _G. C. Greubel_, Sep 22 2019

%p seq((11*n+8)^7, n=0..20); # _G. C. Greubel_, Sep 22 2019

%t (11*Range[0,20]+8)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8, -1}, {2097152, 893871739, 21870000000, 194754273881, 1028071702528, 3938980639167, 12151280273024, 32057708828125}, 20] (* _Harvey P. Dale_, Aug 14 2015 *)

%o (PARI) vector(20, n, (11*n-3)^7) \\ _G. C. Greubel_, Sep 22 2019

%o (Magma) [(11*n+8)^7: n in [0..20]]; // _G. C. Greubel_, Sep 22 2019

%o (Sage) [(11*n+8)^7 for n in (0..20)] # _G. C. Greubel_, Sep 22 2019

%o (GAP) List([0..20], n-> (11*n+8)^7); # _G. C. Greubel_, Sep 22 2019

%Y Powers of the form (11*n+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), A017490 (m=6), this sequence (m=7), A017492 (m=8), A017493 (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms added by _G. C. Greubel_, Sep 22 2019