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Search: id:A090447
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| A090447 |
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Triangle of partial products of binomials. |
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+0
8
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| 1, 1, 1, 1, 2, 2, 1, 3, 9, 9, 1, 4, 24, 96, 96, 1, 5, 50, 500, 2500, 2500, 1, 6, 90, 1800, 27000, 162000, 162000, 1, 7, 147, 5145, 180075, 3781575, 26471025, 26471025, 1, 8, 224, 12544, 878080, 49172480, 1376829440, 11014635520, 11014635520, 1, 9, 324
(list; table; graph; listen)
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OFFSET
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0,5
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LINKS
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W. Lang, First 10 rows.
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FORMULA
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a(n, m)= product(binomial(n, p), p=0..m), n>=m>=0, else 0. Partial row products in Pascal's triangle A007318.
a(n, m)= product(fallfac(n, m-p), p=0..m)/superfac(m), n>=m>=0, else 0; with fallfac(n, m) := A008279(n, m) (falling factorials) and superfac(m)=A000178(m) (superfactorials).
a(n, m)= product((n-p)^(m-p), p=0..m)/superfac(m), n>=m>=0, with 0^0 := 0, else 0.
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EXAMPLE
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[1];[1,1];[1,2,2];[1,3,9,9];...
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CROSSREFS
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Column sequences: A000027 (natural numbers), A006002, A090448-9.
Cf. A090450 (row sums), A090451 (alternating row sums).
Cf. A008949 (partial row sums in Pascal's triangle).
Adjacent sequences: A090444 A090445 A090446 this_sequence A090448 A090449 A090450
Sequence in context: A059584 A136203 A113326 this_sequence A112324 A061531 A071430
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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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