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A090441 Symmetric triangle of certain normalized products of decreasing factorials. 6
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 6, 12, 6, 1, 1, 24, 144, 144, 24, 1, 1, 120, 2880, 8640, 2880, 120, 1, 1, 720, 86400, 1036800, 1036800, 86400, 720, 1, 1, 5040, 3628800, 217728000, 870912000, 217728000, 3628800, 5040, 1, 1, 40320, 203212800, 73156608000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

-1,8

COMMENTS

Similar to, but different from, superfactorial Pascal triangle A009963.

A009963(n,m) = (Product_{p=0..m-1} (n-p)!)/superfac(m) with n >= m >= 0, otherwise 0.

LINKS

Table of n, a(n) for n=-1..47.

Wolfdieter Lang, First 9 rows.

FORMULA

a(n, m) = 0 if n < m-1;

a(n, m) = 1 if m = 0 or n = -1;

a(n, m) = (Product_{p=0..m-1} (n-p)!)/superfac(m-1) if n >= 0, 1 <= m <= n+1, where superfac(n) := A000178(n), n >= 0, (superfactorials).

Equals ConvOffsStoT transform of the factorials, A000142: (1, 1, 2, 6, 24, ...); e.g., ConvOffs transform of (1, 1, 2, 6) = (1, 6, 12, 6, 1). - Gary W. Adamson, Apr 21 2008

EXAMPLE

Rows for n = -1, 0, 1, 2, 3, ...:

  1;

  1,  1;

  1,  1,  1;

  1,  2,  2,  1;

  1,  6, 12,  6,  1;

  ...

CROSSREFS

Column sequences give: A000012 (powers of 1), A000142 (factorials), A010790, A090443-4, etc.

Cf. A090445 (row sums), A090446 (alternating row sums).

Sequence in context: A138169 A139331 A173886 * A340591 A155794 A107876

Adjacent sequences:  A090438 A090439 A090440 * A090442 A090443 A090444

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Dec 23 2003

STATUS

approved

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Last modified July 5 02:59 EDT 2022. Contains 355087 sequences. (Running on oeis4.)