A144108 Eigentriangle based on A052186 (permutations without strong fixed points), row sums = n!

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

Offset

0,7

Comments

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

Left border = A052186.

Links

Table of n, a(n) for n=0..54.

Formula

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,...).

Example

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).

Crossrefs

A000142, Cf. A052186

Sequence in context: A293053 A355652 A355665 * A163972 A068464 A244679

Adjacent sequences: A144105 A144106 A144107 * A144109 A144110 A144111

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 11 2008

Extensions

Typo in row for n=7 corrected by Olivier Gérard, Oct 30 2012

Status

approved