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Search: id:A131198
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| A131198 |
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Triangle T(n,k), 0<=k<=n, read by rows, given by [1,0,1,0,1,0,1,0,...] DELTA [0,1,0,1,0,1,0,1,...] where DELTA is the operator defined in A084938 . |
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+0
7
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| 1, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 6, 6, 1, 0, 1, 10, 20, 10, 1, 0, 1, 15, 50, 50, 15, 1, 0, 1, 21, 105, 175, 105, 21, 1, 0, 1, 28, 196, 490, 490, 196, 28, 1, 0, 1, 36, 336, 1176, 1764, 1176, 336, 36, 1, 0, 1, 45, 540, 2520, 5292, 5292, 2520, 540, 45, 1, 0
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Mirror image of triangle A090181, another version of triangle of Narayana (A001263).
Equals A133336*A130595 as infinite lower triangular matrices . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 23 2007
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FORMULA
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Sum_{k, 0<=k<=n}T(n,k)*x^k = A000012(n), A000108(n), A001003(n), A007564(n), A059231(n), A078009(n), A078018(n), A081178(n), A082147(n), A082181(n), A082148(n), A082173(n) for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 respectively .
Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A000007(n), A000108(n), A006318(n), A047891(n+1), A082298(n), A082301(n), A082302(n), A082305(n), A082366(n), A082367(n), for x = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 respectively . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 23 2007
Sum_{k, 0<=k<=[n/2]}T(n-k,k)=A004148(n). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 06 2007
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EXAMPLE
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Triangle begins:
1;
1, 0;
1, 1, 0;
1, 3, 1, 0;
1, 6, 6, 1, 0;
1, 10, 20, 10, 1, 0;
1, 15, 50, 50, 15, 1, 0;
1, 21, 105, 175, 105, 21, 1, 0;
1, 28, 196, 490, 490, 196, 28, 1, 0 ;...
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CROSSREFS
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Cf. A000217, A002415, A006542, A006857.
Sequence in context: A165253 A059045 A122935 this_sequence A090181 A144417 A085791
Adjacent sequences: A131195 A131196 A131197 this_sequence A131199 A131200 A131201
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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), Oct 20 2007
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