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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 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.)