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Search: id:A133607
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| A133607 |
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Triangle T(n,k), 0<=k<=n, read by rows given by [0, 1, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, -2, 1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . |
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+0
10
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| 1, 0, 1, 0, 1, -1, 0, 1, -1, -1, 0, 1, -1, -2, 1, 0, 1, -1, -3, 2, 1, 0, 1, -1, -4, 3, 3, -1, 0, 1, -1, -5, 4, 6, -3, -1, 0, 1, -1, -6, 5, 10, -6, -4, 1, 0, 1, -1, -7, 6, 15, -10, -10, 4, 1, 0, 1, -1, -8, 7, 21, -15, -20, 10, 5, -1, 0, 1, -1, -9, 8, 28, -21, -35, 20, 15, -5, -1
(list; table; graph; listen)
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OFFSET
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0,14
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COMMENT
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Another version of A108299 ; unsigned version in A103631 (T(n,k)=A103631(n,k)*A057077(k)).
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FORMULA
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Sum_{k, 0<=k<=n}T(n,k)*x^(n-k)= A057077(n), A010892(n), A000012(n), A001519(n), A001835(n), A004253(n), A001653(n), A049685(n-1), A070997(n-1), A070998(n-1), A072256(n), A078922(n), A077417(n-1), A085260(n), A001570(n-1) for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 respectively .
Sum_{k, 0<=k<=n}T(n,k)*x^k = A000007(n), A010892(n), A133631(n), A133665(n), A133666(n), A133667(n), A133668(n), A133669(n), A133671(n), A133672(n) for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 respectively .
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 1, -1;
0, 1, -1, -1;
0, 1, -1, -2, 1;
0, 1, -1, -3, 2, 1;
0, 1, -1, -4, 3, 3, -1;
0, 1, -1, -5, 4, 6, -3, -1;
0, 1, -1, -6, 5, 10, -6, -4, 1;
0, 1, -1, -7, 6, 15, -10, -10, 4, 1;
0, 1, -1, -8, 7, 21, -15, -20, 10, 5, -1;
0, 1, -1, -9, 8, 28, -21, -35, 20, 15, -5, -1;
0, 1, -1, -10, 9, 36, -28, -56, 35, 35, -15, -6, 1 ;...
Triangle A103631 begins:
1;
0, 1;
0, 1, 1;
0, 1, 1, 1;
0, 1, 1, 2, 1;
0, 1, 1, 3, 2, 1;
0, 1, 1, 4, 3, 3, 1;
0, 1, 1, 5, 4, 6, 3, 1;
0, 1, 1, 6, 5, 10, 6, 4, 1;
0, 1, 1, 7, 6, 15, 10, 10, 4, 1;
0, 1, 1, 8, 7, 21, 15, 20, 10, 5, 1;
0, 1, 1, 9, 8, 28, 21, 35, 20, 15, 5, 1;
0, 1, 1, 10, 9, 36, 28, 56, 35, 35, 15, 6, 1 ;...
Triangle A108299 begins:
1;
1, -1;
1, -1, -1;
1, -1, -2, 1;
1, -1, -3, 2, 1;
1, -1, -4, 3, 3, -1;
1, -1, -5, 4, 6, -3, -1;
1, -1, -6, 5, 10, -6, -4, 1;
1, -1, -7, 6, 15, -10, -10, 4, 1;
1, -1, -8, 7, 21, -15, -20, 10, 5, -1;
1, -1, -9, 8, 28, -21, -35, 20, 15, -5, -1;
1, -1, -10, 9, 36, -28, -56, 35, 35, -15, -6, 1 ; ...
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CROSSREFS
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Sequence in context: A080934 A137560 A131255 this_sequence A103631 A083856 A081718
Adjacent sequences: A133604 A133605 A133606 this_sequence A133608 A133609 A133610
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KEYWORD
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sign,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 27 2007
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