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.

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

Links

Table of n, a(n) for n=0..35.

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: A019192 A285624 A356636 * A154912 A133921 A021210

Adjacent sequences: A334954 A334955 A334956 * A334958 A334959 A334960

Keyword

nonn,tabl

Author

Geoffrey Critzer, May 17 2020

Status

approved