A233543 Table T(n,m) = m! read by rows.

1, 1, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 2, 6, 24, 1, 1, 2, 6, 24, 120, 1, 1, 2, 6, 24, 120, 720, 1, 1, 2, 6, 24, 120, 720, 5040, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880

Offset

0,6

Comments

Consider the triangle A193738(n)

1,

1, 1,

1, 2, 2,

1, 2, 3, 3,

1, 2, 3, 4, 4,

1, 2, 3, 4, 5, 5,

1, 2, 3, 4, 5, 6, 6, etc.

The main diagonal is A028310.

The first column of the inverse triangle is

1, -1, 1/2, -1/6, 1/24, -1/120, -1/720,... = 1/e, where e is Euler's number A001113. It is found by

1,

1 - 1 = 0,

1 - 2 + 2/2 = 0,

1 - 2 + 3/2 - 3/6 = 0,

1 - 2 + 3/2 - 4/6 + 4/24 = 0,

1 - 2 + 3/2 - 4/6 + 5/24 - 5/120 = 0,

1 - 2 + 3/2 - 4/6 + 5/24 - 6/120 + 6/720 = 0, etc.

The numerators of this fractional triangle are A193738 signed by rows.

The denominators are a(n).

The denominators of the inverse of A193738(n) are A213936.

Links

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

Formula

T(n,m) = A000142(m).

Example

1,
1, 1,
1, 1, 2,
1, 1, 2, 6
1, 1, 2, 6, 24,
1, 1, 2, 6, 24, 120, etc.

Mathematica

t[_, m_] := m!; Table[Table[t[n, m], {m, 0, n}], {n, 0, 9}] // Flatten (* Jean-François Alcover, Dec 12 2013 *)

Crossrefs

Cf. A166350.

Sequence in context: A246660 A346422 A245405 * A156588 A278543 A374571

Adjacent sequences: A233540 A233541 A233542 * A233544 A233545 A233546

Keyword

nonn,frac,tabl,less

Author

Paul Curtz, Dec 12 2013

Status

approved