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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
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OFFSET
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0,8
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COMMENTS
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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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LINKS
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Table of n, a(n) for n=0..54.
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FORMULA
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T(n, k) = Sum_{j=0..n-k} T(n-1, k-1+j)*A111088(j).
Sum_{k=0..n} T(n, k) = A112934(n).
G.f.: 1/(1-xy/(1-x/(1-2x/(1-3x/(1-4x/(1-... (continued fraction). - Paul Barry, Jan 29 2009
Sum_{k=0..n} T(n,k)*2^(n-k) = A168441(n). - Philippe Deléham, Nov 28 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.
Cf. A084938, A111088, A112934, A168441.
Sequence in context: A085771 A253286 A284799 * A321964 A197819 A232006
Adjacent sequences: A111103 A111104 A111105 * 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 Deléham, Oct 13 2005, Dec 20 2008
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STATUS
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approved
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