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Search: id:A110197
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| A110197 |
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Number triangle of sums of squared binomial coefficients. |
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+0
2
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| 1, 2, 1, 3, 5, 1, 4, 14, 10, 1, 5, 30, 46, 17, 1, 6, 55, 146, 117, 26, 1, 7, 91, 371, 517, 251, 37, 1, 8, 140, 812, 1742, 1476, 478, 50, 1, 9, 204, 1596, 4878, 6376, 3614, 834, 65, 1, 10, 285, 2892, 11934, 22252, 19490, 7890, 1361, 82, 1, 11, 385, 4917, 26334, 66352
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Alternatively, number square T(n,k)=sum{i=0..n, binomial(i+k,k)^2} read by anti-diagonals. Columns include A000027,A000330,A024166,A086020,A086023,A086025. Row sums are A006134. Diagonal sums are A110198.
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FORMULA
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Number triangle T(n, k)=sum{i=0..n-k, binomial(i+k, k)^2}
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EXAMPLE
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Rows start
1;
2,1;
3,5,1;
4,14,10,1;
5,30,46,17,1;
6,55,146,117,26,1;
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CROSSREFS
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Sequence in context: A153277 A104029 A119308 this_sequence A124819 A124019 A125076
Adjacent sequences: A110194 A110195 A110196 this_sequence A110198 A110199 A110200
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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), Jul 15 2005
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