0,4

Triangle read by rows, termwise product of (n-k)! (i.e factorial decrescendo,

A119502) and the INVERT transform of the factorials (A051925) prefaced by a 1:

(1, 1, 2, 5, 15, 54, 235, 1237, 7790,...). A119502 = (1; 1,1; 2,1,1; 6,2,1,1; 24,6,2,1,1;...).

The operation (A051295 * 0^(n-k) with A051295 prefaced with a 1 = an infinite lower triangular matrix with (1, 1, 2, 5, 15, 54, 235,...) in the main diagonal and the rest zeros.

Row sums = the INVERT transform of the factorials, A051295: (1, 2, 5, 15, 54, 235, 1237,...).

Right border shifts A051295: (1, 1, 2, 5, 15,...).

Sum of n-th row terms = rightmost term of next row; e.g. ( 6 + 2 + 2 + 5) = 15.

Factorial eigentriangle: A119502 * (A051295 *0^(n-k); 0<=k<=n

The operation uses A119502 prefaced with a 1 = (1, 1, 2, 5, 15, 54, 235,...);

i.e. the right border of the triangle.

First few rows of the triangle =

1;

1, 1;

2, 1, 2;

6, 2, 2, 5;

24, 6, 4, 5, 15;

120, 24, 12, 10, 15, 54;

720, 120, 48, 30, 30, 54, 235;

5040, 720, 240, 120, 90, 108, 235, 1737;

...

Example: Row 3 = (6, 2, 2, 5) = termwise products of row 3 terms of triangle A119502 (6, 2, 1, 1) and the first four terms of (1, 1, 2, 5,...) = (6*1, 2*1, 1*2, 1*5).

A119502, Cf. A000142, A051295

Sequence in context: A008305 A133644 A152431 this_sequence A098361 A050977 A053448

Adjacent sequences: A143962 A143963 A143964 this_sequence A143966 A143967 A143968

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 06 2008