0,7

Row sums = n!. Sum n-th row terms = rightmost term of next row.

Left border = A052186.

Eigentriangle by rows, T(n,k) = A052186(n-k)*X; 0<=k<=n; where X = an infinite lower triangular matrix with the factorials shifted to (1, 1, 1, 2, 6, 24,...) in the main diagonal and the rest zeros. The triangle A052186 is composed of A052186 in every column: (1, 0, 1, 3, 14, 77, 497,...). The operations are equivalent to (by rows): termwise products of (n+1) terms of A052186 (reversed) and an equal number of terms in the series: (1, 1, 1, 2, 6, 24, 120,...).

First few rows of the triangle =

1;

0, 1;

1, 0, 1;

3, 1, 0, 2;

14, 3, 1, 0, 6;

77, 14, 3, 2, 0, 24;

497, 77, 14, 6, 6, 0, 120;

3676, 497, 77, 28, 18, 24, 0, 720;

30677, 3676, 497, 154, 84, 72, 120, 0, 5040;

285335, 30677, 3676, 994, 462, 336, 360, 720, 0, 40320;

...

Row 3 = (14, 3, 1, 0, 6) = termwise products of (14, 3, 1, 0, 1) and (1, 1, 1, 2, 6) = (14*1, 3*1, 1*1, 0*2, 1*6).

A000142, Cf. A052186

Sequence in context: A119734 A073200 A104416 this_sequence A163972 A068464 A135297

Adjacent sequences: A144105 A144106 A144107 this_sequence A144109 A144110 A144111

nonn,tabl

Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 11 2008