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A121316
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Unlabeled version of A055203: number of different relations between n intervals (of nonzero length) on a line, up to permutation of intervals.
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3
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1, 1, 7, 75, 1105, 20821, 478439, 12977815, 405909913, 14382249193, 569377926495, 24908595049347, 1193272108866953, 62128556769033261, 3493232664307133871, 210943871609662171055, 13615857409567572389361, 935523911378273899335537
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OFFSET
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0,3
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COMMENTS
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Also number of labeled multigraphs without isolated vertices and with n edges.
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LINKS
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FORMULA
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a(n) = (1/n!)* Sum_{k=0..n} |Stirling1(n,k)|*A055203(k).
a(n) = Sum_{k>=0} binomial(k*(k-1)/2+n-1,n)/2^(k+1).
a(n) ~ n^n * 2^(n-1 + log(2)/4) / (exp(n) * (log(2))^(2*n+1)). - Vaclav Kotesovec, Mar 15 2014
a(n) = Sum_{j=0..2*n} binomial(binomial(j,2)+n-1, n) * (Sum_{i=j..2*n} (-1)^(i-j)*binomial(i,j)). - Andrew Howroyd, Feb 09 2020
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MAPLE
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seq(sum(binomial(k*(k-1)/2+n-1, n)/2^(k+1), k=0..infinity), n=0..20);
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MATHEMATICA
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Table[Sum[Binomial[k*(k-1)/2+n-1, n]/2^(k+1), {k, 0, Infinity}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 15 2014 *)
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PROG
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(PARI) a(n) = {sum(j=0, 2*n, binomial(binomial(j, 2)+n-1, n) * sum(i=j, 2*n, (-1)^(i-j)*binomial(i, j)))} \\ Andrew Howroyd, Feb 09 2020
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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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