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A152656 Triangle read by rows: denominators of polynomials from A000142: P(0,x)=1,P(n,x)=1/n!+x*sum(P(n-i-1)/i!),i=0,1,..,n-1. Numerators are A152650. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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 etc.

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: A216914 A216917 A216919 * A096162 A053383 A181538

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

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Last modified March 25 15:02 EDT 2019. Contains 321470 sequences. (Running on oeis4.)