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A334957
Triangular array read by rows. T(n,k) is the number of labeled digraphs on n nodes with exactly k self loops, n>=0, 0<=k<=n.
0
1, 1, 1, 4, 8, 4, 64, 192, 192, 64, 4096, 16384, 24576, 16384, 4096, 1048576, 5242880, 10485760, 10485760, 5242880, 1048576, 1073741824, 6442450944, 16106127360, 21474836480, 16106127360, 6442450944, 1073741824, 4398046511104, 30786325577728, 92358976733184, 153931627888640, 153931627888640, 92358976733184, 30786325577728, 4398046511104
OFFSET
0,4
FORMULA
E.g.f.: g(x + y*x) where g(x) is the e.g.f. for A053763.
EXAMPLE
1,
1, 1,
4, 8, 4,
64, 192, 192, 64,
4096, 16384, 24576, 16384, 4096
MATHEMATICA
nn = 5; g[x_] := Sum[2^(n^2 - n) x^n/n!, {n, 0, nn}]; Map[Select[#, # > 0 &] &, Range[0, nn]! CoefficientList[Series[g[ x + y x], {x, 0, nn}], {x, y}]] // Grid
CROSSREFS
Cf. A053763 (column k=0), A002416 (row sums).
Sequence in context: A376486 A285624 A356636 * A154912 A133921 A021210
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, May 17 2020
STATUS
approved