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A349950
Triangular array read by rows: T(n,k) is the number of partial functions on [n] with exactly k connected components, n>=0, 0<=k<=n.
0
1, 0, 2, 0, 5, 4, 0, 26, 30, 8, 0, 206, 283, 120, 16, 0, 2194, 3360, 1790, 400, 32, 0, 29352, 48538, 29835, 8660, 1200, 64, 0, 472730, 828758, 563486, 193130, 35560, 3360, 128, 0, 8902448, 16352684, 12000604, 4628057, 1023120, 130592, 8960, 256, 0, 191915874, 366387696, 285672572, 120489264, 30357474, 4711392, 442176, 23040, 512
OFFSET
0,3
COMMENTS
Row sums equal (n+1)^n, the number of partial functions on [n].
FORMULA
E.g.f.: exp(y*log(f(x))) where f(x) = 1/(1-t(x))*exp(t(x) and t(x) is the e.g.f. for A000169.
EXAMPLE
1;
0, 2;
0, 5, 4;
0, 26, 30, 8;
0, 206, 283, 120, 16;
0, 2194, 3360, 1790, 400, 32;
...
MATHEMATICA
nn = 10; t[x_] := Sum[n^(n - 1) x^n/n!, {n, 1, nn}]; f[x_] := 1/(1 -t[x])Exp[t[x]]; Table[(Range[0, nn]! CoefficientList[ Series[Exp[y Log[f[x]]], {x, 0, nn}], {x, y}])[[i, 1 ;; i]], {i, 1, nn}] // Grid
CROSSREFS
Cf. A000169 (row sums).
Sequence in context: A324245 A173732 A086280 * A164976 A261745 A083714
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Dec 06 2021
STATUS
approved