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Search: id:A107027
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| A107027 |
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Number triangle associated to the Riordan arrays (1/(1+x),x/(1+x)^k),k>=0. |
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+0
5
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| 1, 1, 2, 1, 2, 2, 1, 2, 4, 2, 1, 2, 6, 8, 2, 1, 2, 8, 20, 16, 2, 1, 2, 10, 38, 70, 32, 2, 1, 2, 12, 62, 196, 252, 64, 2, 1, 2, 14, 92, 426, 1062, 924, 128, 2, 1, 2, 16, 128, 792, 3112, 5948, 3432, 256, 2, 1, 2, 18, 170, 1326, 7302, 23686, 34120, 12870, 512, 2, 1, 2, 20, 218
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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As a number square read by anti-diagonals, the rows represent the row sums of the inverses of the Riordan arrays (1/(1+x),x/(1+x)^k), k>=0. The rows are then given by T(n,k)=(n-1)C(n*k,k)-(n-2)*sum{j=0..k, C(n*k,j)}. T(n,n) is A040000, T(n+1,n) is A000079, T(n+2,n) is A000984, T(n+3,n) is A047098. The reverse of this triangle is A107030. Row sums are A107028. Diagonal sums are A107029.
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FORMULA
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Number triangle T(n, k)=if(k<=n, (n-k-1)C((n-k)*k, k)-(n-k-2)*sum{j=0..k, C((n-k)*k, j)}, 0).
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EXAMPLE
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Triangle begins
1;
1,2;
1,2,2;
1,2,4,2;
1,2,6,8,2;
1,2,8,20,16,2;
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CROSSREFS
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Sequence in context: A140186 A078498 A131240 this_sequence A107030 A050362 A095686
Adjacent sequences: A107024 A107025 A107026 this_sequence A107028 A107029 A107030
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 09 2005
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