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 A107891 a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(3n^2 + 15n + 20)/2880. 7
 1, 19, 155, 805, 3136, 9996, 27468, 67320, 150645, 313027, 611611, 1134497, 2012920, 3436720, 5673648, 9093096, 14194881, 21643755, 32310355, 47319349, 68105576, 96479020, 134699500, 185562000, 252493605, 339663051, 452103939 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Kekulé numbers for certain benzenoids. Partial sums of A114239. First differences of A047819. - Peter Bala, Sep 21 2007 REFERENCES 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). LINKS Shawn A. Broyles, Table of n, a(n) for n = 0..1000 P. Aluffi, Degrees of projections of rank loci, 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]."] FORMULA 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 G.f.: (1+10*x+20*x^2+10*x^3+x^4)/(1-x)^9. - Colin Barker, Feb 08 2012 a(n) = (A000330(n+2)*A000538(n+2) - (A000537(n+2))^2)/4. - J. M. Bergot, Sep 17 2013 MAPLE 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); CROSSREFS Cf. A005585, A006542, A047819, A114239, A114242. Sequence in context: A010825 A022711 A254142 * A302352 A301398 A141923 Adjacent sequences:  A107888 A107889 A107890 * A107892 A107893 A107894 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 12 2005 STATUS approved

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Last modified February 19 22:36 EST 2020. Contains 332061 sequences. (Running on oeis4.)