This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A107891 #50 Sep 02 2024 20:32:49
%S A107891 1,19,155,805,3136,9996,27468,67320,150645,313027,611611,1134497,
%T A107891 2012920,3436720,5673648,9093096,14194881,21643755,32310355,47319349,
%U A107891 68105576,96479020,134699500,185562000,252493605,339663051,452103939
%N A107891 a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(3n^2 + 15n + 20)/2880.
%C A107891 Kekulé numbers for certain benzenoids.
%C A107891 Partial sums of A114239. First differences of A047819. - _Peter Bala_, Sep 21 2007
%D A107891 S. J. Cyvin and I. Gutman, Kekulé structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see pp. 167, 187 and p. 105 eq. (iii) for k=2 and m=5).
%H A107891 Shawn A. Broyles, <a href="/A107891/b107891.txt">Table of n, a(n) for n = 0..1000</a>
%H A107891 Paolo Aluffi, <a href="https://arxiv.org/abs/1408.1702">Degrees of projections of rank loci</a>, arXiv:1408.1702 [math.AG], 2014. ["After compiling the results of many explicit computations, we noticed that many of the numbers d_{n,r,S} appear in the existing literature in contexts far removed from the enumerative geometry of rank conditions; we owe this surprising (to us) observation to perusal of [Slo14]."]
%H A107891 <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 A107891 a(n-2) = (1/8) * Sum_{1 <= x_1, x_2 <= n} (x_1*x_2)^2*(det V(x_1,x_2))^2 = 1/8*sum {1 <= i,j <= n} (i*j*(i-j))^2, where V(x_1,x_2) is the Vandermonde matrix of order 2. - _Peter Bala_, Sep 21 2007
%F A107891 G.f.: (1+10*x+20*x^2+10*x^3+x^4)/(1-x)^9. - _Colin Barker_, Feb 08 2012
%F A107891 a(n) = (A000330(n+2)*A000538(n+2) - (A000537(n+2))^2)/4. - _J. M. Bergot_, Sep 17 2013
%F A107891 Sum_{n>=0} 1/a(n) = 17095/4 - 240*Pi^2 - 162*sqrt(15)*Pi*tanh(sqrt(5/3)*Pi/2). - _Amiram Eldar_, May 29 2022
%p A107891 a:=n->(1/2880)*(n+1)*(n+2)^2*(n+3)^2*(n+4)*(3*n^2+15*n+20): seq(a(n),n=0..32);
%t A107891 Table[((1+n) (2+n)^2 (3+n)^2 (4+n) (20+3 n (5+n)))/2880,{n,0,40}] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,19,155,805,3136,9996,27468,67320,150645},40] (* _Harvey P. Dale_, Dec 10 2021 *)
%Y A107891 Cf. A005585, A006542, A047819, A114239, A114242.
%K A107891 nonn,easy
%O A107891 0,2
%A A107891 _Emeric Deutsch_, Jun 12 2005