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A301566
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a(n) = Sum_{k=1..n-1} k*A088459(n, k).
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1
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0, 2, 15, 82, 405, 1891, 8554, 37850, 164985, 710893, 3036726, 12880847, 54331550, 228089538, 953811972, 3975120810, 16519242465, 68474376025, 283211458750, 1169062910873, 4817380232522, 19819870885230, 81429323786460, 334120527783367, 1369374666890230
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OFFSET
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1,2
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COMMENTS
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a(n)/binomial(2*n-1,n-1) gives the mean distance of the n-odd graph.
Sum can be given in closed form involving four terms each consisting of a product of binomials and 3F2's.
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LINKS
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Eric Weisstein's World of Mathematics, Odd Graph
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FORMULA
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MATHEMATICA
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Table[Sum[k Binomial[n, Ceiling[k/2]] Binomial[n - 1, Floor[k/2]], {k, n - 1}], {n, 20}]
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PROG
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(PARI) T(n, k) = binomial(n, ceil(k/2))*binomial(n-1, k\2);
a(n) = sum(k=1, n-1, k*T(n, k)); \\ Altug Alkan, Mar 23 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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