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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)
0
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
0,5
COMMENTS
Row sums = A062738.
FORMULA
E.g.f.: Log[Sum_{n>=0} (1+y)^(n^2) x^n/n!] + 1
EXAMPLE
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
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
CROSSREFS
Cf. A062735.
Sequence in context: A324057 A106315 A285295 * A373427 A254881 A100946
KEYWORD
nonn,tabf
AUTHOR
Geoffrey Critzer, Oct 07 2012
STATUS
approved