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
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Dec 06 2021
STATUS
approved