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 A070968 Number of cycles in the complete bipartite graph K(n,n). 6
 0, 1, 15, 204, 3940, 113865, 4662231, 256485040, 18226108944, 1623855701385, 177195820499335, 23237493232953516, 3605437233380095620, 653193551573628900289, 136634950180317224866335, 32681589590709963123092160, 8863149183726257535369633856 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Also the number of chordless cycles in the n X n rook graph. - Eric W. Weisstein, Nov 27 2017 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 Eric Weisstein's World of Mathematics, Chordless Cycle Eric Weisstein's World of Mathematics, Complete Bipartite Graph Eric Weisstein's World of Mathematics, Graph Cycle Eric Weisstein's World of Mathematics, Rook Graph FORMULA a(n) = Sum_{k=2..n} C(n,k)^2 * k! * (k-1)! / 2. Recurrence: (n-2)^2*(2*n^3 - 19*n^2 + 58*n - 59)*a(n) = 2*(2*n^7 - 31*n^6 + 200*n^5 - 700*n^4 + 1442*n^3 - 1764*n^2 + 1205*n - 363)*a(n-1) - (n-1)^2*(2*n^7 - 35*n^6 + 266*n^5 - 1139*n^4 + 2962*n^3 - 4671*n^2 + 4130*n - 1578)*a(n-2) + 2*(n-2)^2*(n-1)^2*(2*n^5 - 26*n^4 + 134*n^3 - 342*n^2 + 431*n - 217)*a(n-3) - (n-3)^2*(n-2)^2*(n-1)^2*(2*n^3 - 13*n^2 + 26*n - 18)*a(n-4). - Vaclav Kotesovec, Mar 08 2016 a(n) ~ c * n! * (n-1)!, where c = BesselI(0,2)/2 = 1.1397926511680336337186... . - Vaclav Kotesovec, Mar 08 2016 MAPLE seq(simplify((1/4)*hypergeom([1, 2, 2-n, 2-n], [3], 1)*(n-1)^2*n^2), n=1..20); # Robert Israel, Jan 09 2018 MATHEMATICA Table[Sum[Binomial[n, k]^2*k!*(k - 1)!, {k, 2, n}]/2, {n, 1, 17}] Table[n^2 (HypergeometricPFQ[{1, 1, 1 - n, 1 - n}, {2}, 1] - 1)/2, {n, 20}] (* Eric W. Weisstein, Dec 14 2017 *) PROG (PARI) for(n=1, 50, print1(sum(k=2, n, binomial(n, k)^2 * k! * (k-1)!/2), ", ")) CROSSREFS Cf. A002807, A068087. Sequence in context: A238992 A216465 A215903 * A075280 A093747 A061637 Adjacent sequences:  A070965 A070966 A070967 * A070969 A070970 A070971 KEYWORD nonn AUTHOR Sharon Sela (sharonsela(AT)hotmail.com), May 17 2002 EXTENSIONS More terms from Benoit Cloitre and Robert G. Wilson v, May 20 2002 a(16)-a(17) from Andrew Howroyd, Jan 08 2018 STATUS approved

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Last modified October 28 21:20 EDT 2020. Contains 338064 sequences. (Running on oeis4.)