OFFSET
0,4
COMMENTS
We have two possibilities: with or without 0's.
Without 0's:
1,
1,
1, 2,
1, 12,
1, 50, 24,
1, 180, 360,
etc.
Sum of every row: A000670(n).
First two terms of successive columns: 1, 1, 2, 12, 24, 360, ... = A211374.
With 0's:
1, 0, 0, 0,
1, 0, 0, 0,
1, 2, 0, 0,
1, 12, 0, 0,
1, 50, 24, 0,
1, 180, 360, 0,
1, 602, 3360, 720,
etc.
MATHEMATICA
Derivative[0][y][x] = y[x]; Derivative[1][y][x] = y[x]*(1 - y[x]); Derivative[n_][y][x] := Derivative[n][y][x] = D[Derivative[n - 1][y][x], x]; row[n_] := CoefficientList[Derivative[n][y][x], y[x]] // Rest; Table[ Select[row[n], Positive] , {n, 0, 12}] // Flatten
(* or, simply: *) Table[(-1)^k*k!*StirlingS2[n+1, k+1], {n, 0, 12}, {k, 0, n}] // Flatten // Select[#, Positive]& (* Jean-François Alcover, Dec 16 2014 *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Paul Curtz, Dec 15 2014
STATUS
approved