A217563 Irregular triangular array read by rows. T(n,k) is the number of weakly connected relations on n labeled nodes with k arcs. (n>=0, 0<=k<=n^2).
1, 1, 1, 0, 2, 5, 4, 1, 0, 0, 12, 56, 111, 123, 84, 36, 9, 1, 0, 0, 0, 128, 944, 3264, 7096, 10936, 12687, 11400, 8004, 4368, 1820, 560, 120, 16, 1, 0, 0, 0, 0, 2000, 21104, 109400, 373920, 950725, 1915405, 3168880, 4394760, 5169230, 5188390, 4454000
Offset: 0
Examples
1, 1, 1, 0, 2, 5, 4, 1, 0, 0, 12, 56, 111, 123, 84, 36, 9, 1, 0, 0, 0, 128, 944, 3264, 7096, 10936, 12687, 11400, 8004, 4368, 1820, 560, 120, 16, 1
Crossrefs
Cf. A062735.
Programs
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Mathematica
nn=6; s=Sum[(1+y)^(n^2) x^n/n!, {n,0,nn}]; Range[0,nn]! CoefficientList[Series[ Log[s]+1, {x,0,nn}], {x,y}] //Grid
Formula
E.g.f.: Log[Sum_{n>=0} (1+y)^(n^2) x^n/n!] + 1
Comments