A152656 Triangle read by rows: denominators of polynomials from A000142: P(0,x) = 1, P(n,x) = 1/n! + x*Sum_{i=0..n-1} P(n-i-1)/i!. Numerators are A152650.

1, 1, 1, 2, 1, 1, 6, 1, 1, 1, 24, 3, 2, 1, 1, 120, 3, 2, 1, 1, 1, 720, 15, 8, 3, 2, 1, 1, 5040, 45, 40, 3, 6, 1, 1, 1, 40320, 315, 80, 15, 24, 1, 2, 1, 1, 362880, 315, 560, 45, 24, 1, 6, 1, 1, 1, 3628800, 2835, 4480, 315, 144, 5, 24, 3, 2, 1, 1

Offset: 0

Author

Paul Curtz, Dec 10 2008

Keywords

• nonn
• tabl

Comments

a(n) is the last sequence of a trio with, first, A141412 and, second, A142048 (denominators).

Examples

			Contribution from _Vincenzo Librandi_, Dec 16 2012: (Start)
Triangle begins:
        1,
        1,    1,
        2,    1,    1,
        6,    1,    1,   1,
       24,    3,    2,   1,   1,
      120,    3,    2,   1,   1, 1,
      720,   15,    8,   3,   2, 1,  1,
     5040,   45,   40,   3,   6, 1,  1, 1,
    40320,  315,   80,  15,  24, 1,  2, 1, 1,
   362880,  315,  560,  45,  24, 1,  6, 1, 1, 1,
  3628800, 2835, 4480, 315, 144, 5, 24, 3, 2, 1, 1,
  ...
First column: A000142; second column: A049606. (End)
		

Links

• Vincenzo Librandi, Rows n = 0..100, flattened

Crossrefs

Cf. A152650, A142048, A142412,

Programs

Mathematica

ClearAll[u, p]; u[n_] := 1/n!; p[0][x_] := u[0]; p[n_][x_] := p[n][x] = u[n] + x*Sum[u[i]*p[n-i-1][x] , {i, 0, n-1}] // Expand; row[n_] := CoefficientList[p[n][x], x]; Table[row[n], {n, 0, 10}] // Flatten // Denominator (* Jean-François Alcover, Oct 02 2012 *)

Extensions

More terms from Jean-François Alcover, Oct 02 2012