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Search: id:A090441
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| A090441 |
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Symmetric triangle of certain normalized products of decreasing factorials. |
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+0
6
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| 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; listen)
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OFFSET
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-1,8
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COMMENT
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Similar to, but different from, superfactorial Pascal triangle A009963.
A009963(n,m)= product((n-p)!,p=0..m-1)/superfac(m) with n>=m>=0 else 0.
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LINKS
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W. Lang, First 9 rows.
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FORMULA
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a(n, m)=0 if n< m-1; a(n, m)=1 if m=0 or n=-1; a(n, m)= product((n-p)!, p=0..m-1)/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 (qntmpkt(AT)yahoo.com), Apr 21 2008
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EXAMPLE
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[1];[1,1];[1,1,1];[1,2,2,1];[1,6,12,6,1];..., rows for
n=-1,0,1,2,3,...
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CROSSREFS
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Column sequences give: A000012 (powers of 1), A000142 (factorials), A010790, A090443-4, etc.
Cf. A090445 (row sums), A090446 (alternating row sums).
Adjacent sequences: A090438 A090439 A090440 this_sequence A090442 A090443 A090444
Sequence in context: A135879 A138169 A139331 this_sequence A107876 A121554 A011296
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Dec 23 2003
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