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Search: id:A120730
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| 1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 2, 3, 1, 0, 0, 0, 5, 4, 1, 0, 0, 0, 5, 9, 5, 1, 0, 0, 0, 0, 14, 14, 6, 1, 0, 0, 0, 0, 14, 28, 20, 7, 1, 0, 0, 0, 0, 0, 42, 48, 27, 8, 1, 0, 0, 0, 0, 0, 42, 90, 75, 35, 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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Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 1, -1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, ...] DELTA [1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1, ...] where DELTA is the operator defined in A084938.
Aerated version gives A165408. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 22 2009]
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FORMULA
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Sum_{k, 0<=k<=n}x^k*T(n,n-k)= A001405(n), A126087(n), A128386(n), A121724(n), A128387(n), A132373(n), A132374(n), A132375(n), A121725(n) for x=1,2,3,4,5,6,7,8,9 respectively .
T(2*n,n)= A000108(n); A000108 : Catalan numbers.
Sum_{k, 0<=k<=n}T(n,k)^2 = A000108(n) and Sum_{n, n>=k}T(n,k) = A000108(k+1). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2008]
Sum_{k, 0<=k<=n}T(n,k)^3 = A003161(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2008]
Sum_{k, 0<=k<=n}T(n,k)^4 = A129123(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2008]
Sum{k=0..n, T(n,k)*x^k}= A000007(n), A001405(n), A151281(n), A151162(n), A151254(n), A156195(n), A156361(n), A156362(n), A156566(n), A156577(n) for x=0,1,2,3,4,5,6,7,8,9 respectively. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 10 2009]
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EXAMPLE
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As a triangle, this begins:
1;
0, 1;
0, 1, 1;
0, 0, 2, 1;
0, 0, 2, 3, 1;
0, 0, 0, 5, 4, 1;
0, 0, 0, 5, 9, 5, 1;
0, 0, 0, 0, 14, 14, 6, 1;
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CROSSREFS
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Sequence in context: A058626 A122856 A055791 this_sequence A122851 A064301 A060701
Adjacent sequences: A120727 A120728 A120729 this_sequence A120731 A120732 A120733
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KEYWORD
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nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 17 2006, corrected Sep 15 2006
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EXTENSIONS
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Corrected formula . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2008
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