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a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)^2*(n+5)(3n^2 + 13n + 15)/43200.
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%I #12 Jun 13 2015 00:51:50

%S 1,31,371,2646,13524,54684,185724,551034,1467609,3578575,8107099,

%T 17257604,34826064,67098864,124140528,221594796,383151321,643861911,

%U 1054526011,1687405258,2643571700,4062243900,6132519900,9107976150,13324667265,19223133111,27375097491

%N a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)^2*(n+5)(3n^2 + 13n + 15)/43200.

%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. 229).

%H T. D. Noe, <a href="/A107941/b107941.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

%F G.f.: (1+20*x+85*x^2+105*x^3+38*x^4+3*x^5)/(1-x)^11. - _Colin Barker_, Sep 18 2012

%p a:=n->(1/43200)*(n+1)*(n+2)^2*(n+3)^2*(n+4)^2*(n+5)*(3*n^2+13*n+15): seq(a(n),n=0..28);

%K nonn,easy

%O 0,2

%A _Emeric Deutsch_, Jun 12 2005