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 A107915 a(n) = binomial(n+4,4)*binomial(n+5,4)*binomial(n+6,4)/75. 5
 1, 35, 490, 4116, 24696, 116424, 457380, 1557270, 4723719, 13026013, 33157124, 78835120, 176729280, 376375104, 766192176, 1498581756, 2828205765, 5168991135, 9177226366, 15870391460, 26794167400, 44253495000, 71627692500, 113794603650, 177694650315 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS KekulĂ© numbers for certain benzenoids. Partial sums of A107917. - Peter Bala, Sep 21 2007 REFERENCES S. J. Cyvin and I. Gutman, KekulĂ© structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (p. 229). LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 FORMULA a(n) = C(n,n-2)*C(n+1,n-3)*C(n+2,n-4)/(5*3!), n>=4. - Zerinvary Lajos, May 29 2007 a(n-3) = 1/144*sum {1 <= x_1, x_2, x_3 <= n} x_1*x_2*x_3*(det V(x_1,x_2,x_3))^2 = 1/144*sum {1 <= i,j,k <= n} i*j*k*((i-j)(i-k)(j-k))^2, where V(x_1,x_2,x_3) is the Vandermonde matrix of order 3. - Peter Bala, Sep 21 2007 G.f.: -(x^6+22*x^5+113*x^4+190*x^3+113*x^2+22*x+1)/(x-1)^13. - Colin Barker, Jun 06 2012 MAPLE a:=n->(1/75)*binomial(n+4, 4)*binomial(n+5, 4)*binomial(n+6, 4): seq(a(n), n=0..27); seq(binomial(n, n-2)*binomial(n+1, n-3)*binomial(n+2, n-4)/(5*3!), n=4..22); # Zerinvary Lajos, May 29 2007 CROSSREFS Cf. A047819, A107917, A133708. Sequence in context: A298946 A219582 A177079 * A219370 A278674 A219468 Adjacent sequences:  A107912 A107913 A107914 * A107916 A107917 A107918 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jun 12 2005 STATUS approved

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Last modified September 22 22:24 EDT 2020. Contains 337291 sequences. (Running on oeis4.)