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a(n) = 10(n+1)^3*(2n+1)(7n+5)^2.
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%I #11 Feb 22 2020 20:40:03

%S 250,34560,487350,3028480,12251250,38016000,98499310,223948800,

%T 461143530,878560000,1572243750,2672386560,4350609250,6827950080,

%U 10383558750,15364096000,22193838810,31385491200,43551700630

%N a(n) = 10(n+1)^3*(2n+1)(7n+5)^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 <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.: 10(25 + 3281z + 25068z^2 + 33404z^3 + 8539z^4 + 243z^5)/(1-z)^7.

%p a:=n->10*(n+1)^3*(2*n+1)*(7*n+5)^2: seq(a(n),n=0..28);

%t Table[10(n+1)^3(2n+1)(7n+5)^2,{n,0,30}] (* _Harvey P. Dale_, Aug 07 2019 *)

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Jun 19 2005