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A173424
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Triangle T(n,m) read by rows: (2*n - 2*m)!*(2*m)!/( 2^n*(n - m)!*m! )
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0
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1, 1, 1, 3, 1, 3, 15, 3, 3, 15, 105, 15, 9, 15, 105, 945, 105, 45, 45, 105, 945, 10395, 945, 315, 225, 315, 945, 10395, 135135, 10395, 2835, 1575, 1575, 2835, 10395, 135135, 2027025, 135135, 31185, 14175, 11025, 14175, 31185, 135135, 2027025, 34459425
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OFFSET
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0,4
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COMMENTS
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Row sums are: 1, 2, 7, 36, 249, 2190, 23535, 299880, 4426065, 74294010, 1397669175, ..., apparently A034430.
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LINKS
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Table of n, a(n) for n=0..45.
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FORMULA
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T(n,m)= A006882(2*n-2*m-1)* A006882(2*m-1) = A001147(n-m)*A001147(m).
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EXAMPLE
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1;
1, 1;
3, 1, 3;
15, 3, 3, 15;
105, 15, 9, 15, 105;
945, 105, 45, 45, 105, 945;
10395, 945, 315, 225, 315, 945, 10395;
135135, 10395, 2835, 1575, 1575, 2835, 10395, 135135;
2027025, 135135, 31185, 14175, 11025, 14175, 31185, 135135, 2027025;
34459425, 2027025, 405405, 155925, 99225, 99225, 155925, 405405, 2027025, 34459425;
654729075, 34459425, 6081075, 2027025, 1091475, 893025, 1091475, 2027025, 6081075, 34459425, 654729075;
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MATHEMATICA
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t[n_, m_] = (2*n - 2*m)!*(2*m)!/(2^n*(n - m)!*m!);
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
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Sequence in context: A351372 A356411 A355793 * A143081 A179658 A112811
Adjacent sequences: A173421 A173422 A173423 * A173425 A173426 A173427
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula, Feb 18 2010
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EXTENSIONS
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Formula added by the Assoc. Editors of the OEIS, Feb 24 2010
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STATUS
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approved
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