|
%I #17 Oct 19 2023 07:37:04
%S 1,26,250,1435,5978,19992,56952,143550,328515,695266,1379378,2591953,
%T 4650100,8015840,13344864,21546684,33857829,51929850,77934010,
%U 114684647,165783310,235785880,330395000,456680250,623328615,840927906,1122285906
%N a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(2*n^2 + 6*n + 5)/720.
%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. 230, no. 21).
%H Harvey P. Dale, <a href="/A108645/b108645.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F G.f.: (1+17*x+52*x^2+37*x^3+5*x^4)/(1-x)^9. - _Harvey P. Dale_, Sep 05 2016
%F E.g.f.: (1/6!)*(720 + 18000*x + 71640*x^2 + 91440*x^3 + 49050*x^4 + 12486*x^5 + 1565*x^6 + 92*x^7 + 2*x^8)*exp(x). - _G. C. Greubel_, Oct 19 2023
%p a:=(n+1)*(n+2)^2*(n+3)^2*(n+4)*(2*n^2+6*n+5)/720: seq(a(n),n=0..30);
%t Table[(n+1)(n+2)^2(n+3)^2(n+4)(2n^2+6n+5)/720,{n,0,30}] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,26,250,1435, 5978,19992,56952,143550,328515},30] (* _Harvey P. Dale_, Sep 05 2016 *)
%o (Magma) B:=Binomial; [(2*n^2+6*n+5)*B(n+4,4)*B(n+3,2)/15: n in [0..40]]; // _G. C. Greubel_, Oct 19 2023
%o (SageMath) b=binomial; [(2*n^2+6*n+5)*b(n+4,4)*b(n+3,2)/15 for n in range(41)] # _G. C. Greubel_, Oct 19 2023
%Y Cf. A108646, A108647, A108648, A108649, A108650.
%K nonn
%O 0,2
%A _Emeric Deutsch_, Jun 13 2005
|
