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

0,4

Comments

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

Links

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

Example

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)

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 *)

Crossrefs

Cf. A152650, A142048, A142412,

Sequence in context: A216917 A320637 A216919 * A096162 A333144 A306297

Adjacent sequences: A152653 A152654 A152655 * A152657 A152658 A152659

Keyword

nonn,tabl

Author

Paul Curtz, Dec 10 2008

Extensions

More terms from Jean-François Alcover, Oct 02 2012

Status

approved