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a(n) = 10*(n+1)^3*(n+2)*(5*n+7)^2.
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%I #21 Jan 20 2024 19:45:26

%S 980,34560,312120,1548800,5467500,15482880,37565360,81285120,

%T 161036100,297440000,518930280,863516160,1380726620,2133734400,

%U 3201660000,4682055680,6693569460,9378789120,12907266200,17478720000,23326421580,30720757760,39972975120,51439104000

%N a(n) = 10*(n+1)^3*(n+2)*(5*n+7)^2.

%C Kekulé numbers for certain benzenoids.

%D S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 311).

%H G. C. Greubel, <a href="/A109120/b109120.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F G.f.: 20*(49 + 1385*z + 4539*z^2 + 2771*z^3 + 256*z^4)/(1-z)^7.

%F E.g.f.: 10*(98 + 3358*x + 12199*x^2 + 11919*x^3 + 4199*x^4 + 570*x^5 + 25*x^6)*exp(x). - _G. C. Greubel_, Feb 09 2020

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - _Wesley Ivan Hurt_, Aug 19 2022

%p a:=n->10*(n+1)^3*(n+2)*(5*n+7)^2: seq(a(n),n=0..30);

%t Table[10(n+1)^3(n+2)(5n+7)^2,{n,0,30}]

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{980,34560,312120,1548800,5467500,15482880,37565360},30] (* _Harvey P. Dale_, Jan 20 2024 *)

%o (PARI) vector(31, n, my(m=n-1); 10*(m+1)^3*(m+2)*(5*m+7)^2) \\ _G. C. Greubel_, Feb 09 2020

%o (Magma) [10*(n+1)^3*(n+2)*(5*n+7)^2: n in [0..30]]; // _G. C. Greubel_, Feb 09 2020

%o (Sage) [10*(n+1)^3*(n+2)*(5*n+7)^2 for n in (0..30)] # _G. C. Greubel_, Feb 09 2020

%o (GAP) List([0..30], n-> 10*(n+1)^3*(n+2)*(5*n+7)^2 ); # _G. C. Greubel_, Feb 09 2020

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Jun 19 2005