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 A098909 Triangle T(n,k) of numbers of connected (unicyclic) graphs with unique cycle of length k (3<=k<=n), on n labeled nodes. 4
 1, 12, 3, 150, 60, 12, 2160, 1080, 360, 60, 36015, 20580, 8820, 2520, 360, 688128, 430080, 215040, 80640, 20160, 2520, 14880348, 9920232, 5511240, 2449440, 816480, 181440, 20160, 360000000, 252000000, 151200000, 75600000, 30240000, 9072000 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS G. C. Greubel, Rows n = 3..100 of triangle, flattened FORMULA T(n, k) = (n-1)!*n^(n-k)/(2*(n-k)!). E.g.f.: -(2*log(1+x*LambertW(-y))-2*x*LambertW(-y)+x^2*LambertW(-y)^2)/4. EXAMPLE Triangle begins as: 1; 12, 3; 150, 60, 12; 2160, 1080, 360, 60; 36015, 20580, 8820, 2520, 360; ... MATHEMATICA f[list_] := Select[list, #>0&]; t = Sum[n^(n-1)x^n/n!, {n, 1, 20}]; Map[f, Drop[Transpose[Table[Range[0, 8]! CoefficientList[Series[t^n/(2n), {x, 0, 8}], x], {n, 3, 8}]], 3]] (* Geoffrey Critzer, Oct 23 2011 *) Table[k!*Binomial[n, k]*n^(n-k-1)/2, {n, 3, 12}, {k, 3, n}]//Flatten (* G. C. Greubel, May 16 2019 *) PROG (PARI) {T(n, k) = k!*binomial(n, k)*n^(n-k-1)/2 }; \\ G. C. Greubel, May 16 2019 (Magma) [[Factorial(k)*Binomial(n, k)*n^(n-k-1)/2: k in [3..n]]: n in [3..12]]; // G. C. Greubel, May 16 2019 (Sage) [[factorial(k)*binomial(n, k)*n^(n-k-1)/2 for k in (3..n)] for n in (3..12)] # G. C. Greubel, May 16 2019 (GAP) Flat(List([3..12], n-> List([3..n], k-> Factorial(k)*Binomial(n, k) *n^(n-k-1)/2 ))); # G. C. Greubel, May 16 2019 CROSSREFS Row sums: A057500, columns: A053507, A065889. Sequence in context: A258227 A130895 A038329 * A261403 A010202 A079792 Adjacent sequences: A098906 A098907 A098908 * A098910 A098911 A098912 KEYWORD easy,nonn,tabl AUTHOR Vladeta Jovovic, Oct 15 2004 STATUS approved

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Last modified May 31 12:12 EDT 2023. Contains 363066 sequences. (Running on oeis4.)