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Search: id:A133336
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| A133336 |
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Triangle T(n,k), 0<=k<=n, read by rows, given by [1,1,1,1,1,1,1,...] DELTA [0,1,0,1,0,1,0,1,0,...] where DELTA is the operator defined in A084938 . |
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+0
7
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| 1, 1, 0, 2, 1, 0, 5, 5, 1, 0, 14, 21, 9, 1, 0, 42, 84, 56, 14, 1, 0, 132, 330, 300, 120, 20, 1, 0, 429, 1287, 1485, 825, 225, 27, 1, 0, 1430, 5005, 7007, 5005, 1925, 385, 35, 1, 0, 4862, 19448, 32032, 28028, 14014, 4004, 616, 44, 1, 0, 16796, 75582, 143208, 148512
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Mirror image of triangle A086810 ; another version of A126216 .
Equals A131198*A007318 as infinite lower triangular matrices . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 23 2007
Diagonal sums : A119370. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 09 2009]
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REFERENCES
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W. Y. C. Chen, T. Mansour and S. H. Yan, Matchings avoiding partial patterns, The Electronic Journal of Combinatorics 13, 2006, #R112, Theorem 3.3 .
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FORMULA
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Sum_{k, 0<=k<=n}T(n,k)*x^k = 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 respectively .
Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A000007(n), A001003(n), A107841(n), A131763(n), A131765(n), A131846(n), A131926(n), A131869(n), A131927(n) for x = 0, 1, 2, 3, 4, 5, 6, 7, 8 respectively . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 05 2007
Sum_{k, 0<=k<=n}T(n,k)*(-2)^k*5^(n-k) = A152601(n). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 10 2008]
T(n,k)= binomial(n-1,k)*binomial(2n-k,n)/(n+1), k<=n. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2009]
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EXAMPLE
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Triangle begins:
1;
1, 0;
2, 1, 0;
5, 5, 1, 0;
14, 21, 9, 1, 0;
42, 84, 56, 14, 1, 0;
132, 330, 300, 120, 20, 1, 0;
429, 1287, 1485, 825, 225, 27, 1, 0;
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CROSSREFS
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Cf. A000108, A002054, A002055, A002056, A007160, A033280, A033281, A033282.
Sequence in context: A113368 A066435 A030206 this_sequence A130191 A059720 A140589
Adjacent sequences: A133333 A133334 A133335 this_sequence A133337 A133338 A133339
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KEYWORD
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nonn,tabl,new
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 19 2007
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