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 A107915 a(n) = binomial(n+4,4)*binomial(n+5,4)*binomial(n+6,4)/75. 7
 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 Kekulé numbers for certain benzenoids. Partial sums of A107917. - 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 (p. 229). LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 Stefan Felsner, Eric Fusy, Marc Noy, and David Orden, Bijections for Baxter families and related objects, J. Combin. Theory Ser. A, 118(3):993-1020, 2011. 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 From Amiram Eldar, May 29 2022: (Start) Sum_{n>=0} 1/a(n) = 25200*Pi^2 - 248713. Sum_{n>=0} (-1)^n/a(n) = 376003 - 430080*log(2) - 64800*zeta(3). (End) 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 MATHEMATICA a[n_] := Binomial[n + 4, 4] * Binomial[n + 5, 4] * Binomial[n + 6, 4]/75; Array[a, 25, 0] (* Amiram Eldar, May 29 2022 *) 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 8 08:54 EDT 2024. Contains 375753 sequences. (Running on oeis4.)