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%I #10 Sep 06 2017 20:55:27
%S 1,45,632,4825,25227,101822,340416,986094,2551725,6028099,13209768,
%T 27179087,53000311,98685900,176508416,304743564,509943033,829849833,
%U 1317083800,2043740853,3107066435,4636381354,6801456960,9822556250
%N 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 (see p. 243, H*(4,4,n)).
%H G. C. Greubel, <a href="/A110691/b110691.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = (n+1)*(n+2)^3*(n+3)*(13*n^4 + 104*n^3 + 311*n^2 + 412*n + 210)/7!.
%F G.f.: (x^6+35*x^5+227*x^4+410*x^3+227*x^2+35*x+1)/(1-x)^10. - _Alois P. Heinz_, Feb 27 2015
%p a:=n->(n+1)*(n+2)^3*(n+3)*(13*n^4+104*n^3+311*n^2+412*n+210)/5040: seq(a(n),n=0..25);
%t CoefficientList[Series[(x^6 + 35*x^5 + 227*x^4 + 410*x^3 + 227*x^2 + 35*x + 1)/(x - 1)^10, {x, 0, 50}], x] (* _G. C. Greubel_, Sep 06 2017 *)
%o (PARI) x='x+O('x^50); Vec((x^6+35*x^5+227*x^4+410*x^3+227*x^2+35*x+1)/(1-x)^10) \\ _G. C. Greubel_, Sep 06 2017
%K nonn,easy
%O 0,2
%A _Emeric Deutsch_, Aug 03 2005
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