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 A065889 a(n) = number of unicyclic connected simple graphs whose cycle has length 4. 5
 3, 60, 1080, 20580, 430080, 9920232, 252000000, 7015381560, 212840939520, 6998969586180, 248180493969408, 9445533398437500, 384213343210045440, 16639691095281974160, 764619269867445288960, 37163398969133506235952 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 4..150 FORMULA E.g.f.: T^4/8, where T = T(x) is Euler's tree function (see A000169). a(n) = (n-1)*(n-2)*(n-3)*n^(n-4)/2. - Vladeta Jovovic, Oct 26 2004 MATHEMATICA Table[12*Binomial[n, 4]*n^(n-5), {n, 4, 25}] (* G. C. Greubel, May 16 2019 *) PROG (PARI) {a(n) = 12*binomial(n, 4)*n^(n-5)}; \\ G. C. Greubel, May 16 2019 (MAGMA) [12*Binomial(n, 4)*n^(n-5) : n in [4..25]]; // G. C. Greubel, May 16 2019 (Sage) [12*binomial(n, 4)*n^(n-5) for n in (4..25)] # G. C. Greubel, May 16 2019 (GAP) List([4..25], n-> 12*Binomial(n, 4)*n^(n-5)) # G. C. Greubel, May 16 2019 CROSSREFS A065888 ( = 2*A065889) counts sagittal graphs with one cycle (length 4). A column of A098909, A053507. Main diagonal of A144209. Sequence in context: A195550 A144659 A115490 * A183251 A001084 A137150 Adjacent sequences:  A065886 A065887 A065888 * A065890 A065891 A065892 KEYWORD nonn AUTHOR Len Smiley, Nov 27 2001 STATUS approved

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Last modified October 18 17:13 EDT 2019. Contains 328186 sequences. (Running on oeis4.)