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Search: id:A113139
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| A113139 |
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Number triangle, equal to half of Delannoy square array A008288. |
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+0
3
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| 1, 3, 1, 13, 5, 1, 63, 25, 7, 1, 321, 129, 41, 9, 1, 1683, 681, 231, 61, 11, 1, 8989, 3653, 1289, 377, 85, 13, 1, 48639, 19825, 7183, 2241, 575, 113, 15, 1, 265729, 108545, 40081, 13073, 3649, 833, 145, 17, 1, 1462563, 598417, 224143, 75517, 22363, 5641
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums are A047781(n+1). Diagonal sums are A113140. Inverse is A113141.
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FORMULA
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T(n, k)=sum{j=0..n, C(n-k, j)C(n+j, k+j)}; T(n, k)=sum{j=0..n, C(n, j)C(n-k, j-k)2^(n-j)};
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EXAMPLE
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Triangle begins
1;
3, 1;
13, 5, 1;
63, 25, 7, 1;
321, 129, 41, 9, 1;
1683,681, 231, 61, 11, 1;
8989,3653,1289,377,85, 13, 1;
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CROSSREFS
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Sequence in context: A019232 A016479 A134768 this_sequence A143411 A096773 A118384
Adjacent sequences: A113136 A113137 A113138 this_sequence A113140 A113141 A113142
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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), Oct 15 2005
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