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Search: id:A117207
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| A117207 |
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Number triangle T(n,k)=sum{j=0..n-k, C(n+j,j+k)C(n-j,k)}. |
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+0
1
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| 1, 3, 1, 10, 7, 1, 35, 31, 13, 1, 126, 121, 81, 21, 1, 462, 456, 381, 181, 31, 1, 1716, 1709, 1583, 1058, 358, 43, 1, 6435, 6427, 6231, 5055, 2605, 645, 57, 1, 24310, 24301, 24013, 21661, 14605, 5785, 1081, 73, 1, 92378, 92368, 91963, 87643, 70003, 38251, 11791
(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 A037965(n+1).
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FORMULA
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T(n,k)=C(2n+1,n+1)-sum{j=1..k, product{i=0..j-2, (n-i)^2}/((j-1)!j!)}}*(n+1)
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EXAMPLE
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Triangle begins
1,
3, 1,
10, 7, 1,
35, 31, 13, 1,
126, 121, 81, 21, 1,
462, 456, 381, 181, 31, 1,
1716, 1709, 1583, 1058, 358, 43, 1
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CROSSREFS
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Sequence in context: A091965 A107056 A116384 this_sequence A046658 A124574 A052964
Adjacent sequences: A117204 A117205 A117206 this_sequence A117208 A117209 A117210
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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), Mar 02 2006
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