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%I A300850 #12 Mar 13 2018 22:12:57
%S A300850 0,0,10,105,840,5775,36036,210210,1166880,6235515,32332300,163601438,
%T A300850 811246800,3954828150,19001896200,90162058500,423160594560,
%U A300850 1967035576275,9066060164700,41468830753350,188390256054000,850582006083810,3818939619151800,17058982348359900
%N A300850 Number of 6-cycles in the n-odd graph.
%H A300850 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>
%H A300850 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OddGraph.html">Odd Graph</a>
%F A300850 a(n) = binomial(2*n-1, n-1)*n*(n-1)^2/12 for n > 2. - _Andrew Howroyd_, Mar 13 2018
%F A300850 From _Robert Israel_, Mar 13 2018: (Start)
%F A300850 G.f.: x^2*(1+6*x)/(2*(1-4*x)^(7/2))-x^2/2.
%F A300850 (12+24*n)*a(n)+(22-2*n)*a(n+1)-n*a(n+2)=0. (End)
%p A300850 0,0,seq(binomial(2*n-1, n-1)*n*(n-1)^2/12, n=3..40); # _Robert Israel_, Mar 13 2018
%t A300850 Join[{0, 0}, Table[Binomial[2 n - 1, n - 1] n (n - 1)^2/12, {n, 3, 18}]]
%t A300850 CoefficientList[Series[x (1/(1 - 4 x)^(7/2) + (6 x)/(1 - 4 x)^(7/2) - 1)/2, {x, 0, 20}], x]
%t A300850 Join[{0, 0}, RecurrenceTable[{(12 + 24 n) a[n] + (22 - 2 n) a[n + 1] == n a[n + 2], a[3] == 10, a[4] == 105}, a, {n, 3, 20}]]
%o A300850 (PARI) a(n)={if(n==2, 0, binomial(2*n-1, n-1)*n*(n-1)^2/12)} \\ _Andrew Howroyd_, Mar 13 2018
%K A300850 nonn
%O A300850 1,3
%A A300850 _Eric W. Weisstein_, Mar 13 2018
%E A300850 Terms a(8) and beyond from _Andrew Howroyd_, Mar 13 2018

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