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Search: id:A119328
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| A119328 |
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Number triangle T(n,k)=sum{i=0..n, (-1)^(n-i)*C(n,i)*sum{j=0..i-k, C(k,2j)*C(i-k,2j)}}. |
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+0
3
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| 1, 0, 1, 0, -1, 1, 0, 1, -2, 1, 0, -1, 4, -3, 1, 0, 1, -6, 9, -4, 1, 0, -1, 8, -19, 16, -5, 1, 0, 1, -10, 33, -44, 25, -6, 1, 0, -1, 12, -51, 96, -85, 36, -7, 1, 0, 1, -14, 73, -180, 225, -146, 49, -8, 1, 0, -1, 16, -99, 304, -501, 456, -231, 64, -9, 1
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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Row sums are A021913(n+2). Product with Pascal's triangle A007318 is A119326. A signed version of A058716.
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FORMULA
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Column k has g.f. (x/(1+x))^k*sum{j=0..k, C(k,2j)x^(2j)}
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EXAMPLE
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Triangle begins
1,
0, 1,
0, -1, 1,
0, 1, -2, 1,
0, -1, 4, -3, 1,
0, 1, -6, 9, -4, 1,
0, -1, 8, -19, 16, -5, 1,
0, 1, -10, 33, -44, 25, -6, 1,
0, -1, 12, -51, 96, -85, 36, -7, 1,
0, 1, -14, 73, -180, 225, -146, 49, -8, 1,
0, -1, 16, -99, 304, -501, 456, -231, 64, -9, 1
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CROSSREFS
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Sequence in context: A034369 A055277 A055340 this_sequence A058716 A048723 A088455
Adjacent sequences: A119325 A119326 A119327 this_sequence A119329 A119330 A119331
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 14 2006
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