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Search: id:A111106
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| A111106 |
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Riordan array (1,x*g(x)) where g(x) is g.f. of double factorials A001147. |
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4
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| 1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 15, 7, 3, 1, 0, 105, 36, 12, 4, 1, 0, 945, 249, 64, 18, 5, 1, 0, 10395, 2190, 441, 100, 25, 6, 1, 0, 135135, 23535, 3807, 691, 145, 33, 7, 1, 0, 2027025, 299880, 40032, 5880, 1010, 200, 42, 8, 1
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Triangle T(n,k), 0<=k<=n, given by [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
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FORMULA
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T(n, k) = Sum_{j, 0<=j<=n-k} T(n-1, k-1+j)*A111088(j).
Sum_{k, 0<=k<=n} T(n, k) = A112934(n).
G.f.: 1/(1-xy/(1-x/(1-2x/(1-3x/(1-4x/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Jan 29 2009]
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EXAMPLE
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Rows begin:
1;
0, 1;
0, 1, 1;
0, 3, 2, 1;
0, 15, 7, 3, 1;
0, 105, 36, 12, 4, 1;
0, 945, 249, 64, 18, 5, 1;
0, 10395, 2190, 441, 100, 25, 6, 1:
0, 135135, 23535, 3807, 691, 145, 33, 7, 1;
0, 2027025, 299880, 40032, 5880, 1010, 200, 42, 8, 1;
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CROSSREFS
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Columns : A000007, A001147, A034430 ; Diagonals : A000012, A001477, A055998,
Sequence in context: A035327 A004444 A085771 this_sequence A113081 A109865 A096874
Adjacent sequences: A111103 A111104 A111105 this_sequence A111107 A111108 A111109
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 13 2005, Dec 20 2008
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