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Search: id:A129818
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| A129818 |
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Riordan array (1/(1+x),x/(1+x)^2), inverse array is A039599 . |
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5
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| 1, -1, 1, 1, -3, 1, -1, 6, -5, 1, 1, -10, 15, -7, 1, -1, 15, -35, 28, -9, 1, 1, -21, 70, -84, 45, -11, 1, -1, 28, -126, 210, -165, 66, -13, 1, 1, -36, 210, -462, 495, -286, 91, -15, 1, -1, 45, -330, 924, -1287, 1001, -455, 120, 120, -17, 1, 1, -55, 495, -1716, 3003, -3003, 1820, -680, 153, -19, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums : A057078 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 11 2007
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REFERENCES
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Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
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FORMULA
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T(n,k)=(-1)^(n-k)*A085478(n,k)= (-1)^(n-k)*binomial(n+k,2*k) .
Sum_{k, 0<=k<=n}T(n,k)*A000531(k)=n^2, with A000531(0)=0 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 11 2007
Sum_{k, 0<=k<=n}T(n,k)*x^k = A033999(n), A057078(n), A057077(n), A057079(n), A005408(n), A001906(n), A001834(n), A030221(n), A002315(n), A033890(n), A057080(n), A057081(n), A054320(n), A097783(n), A077416(n), A126866(n), A028230(n+1) for x = 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16 respectively. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2009]
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EXAMPLE
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Triangle begins:
1;
-1, 1;
1, -3, 1;
-1, 6, -5, 1;
1, -10, 15, -7, 1;
-1, 15, -35, 28, -9, 1;
1, -21, 70, -84, 45, -11, 1;
-1, 28, -126, 210, -165, 66, -13, 1;
1, -36, 210, -462, 495, -286, 91, -15, 1;
-1, 45, -330, 924, -1287, 1001, -455, 120, -17, 1;
1, -55, 495, -1716, 3003, -3003, 1820, -680, 153, -19, 1 ;...
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CROSSREFS
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Sequence in context: A103141 A085478 A123970 this_sequence A055898 A145904 A159572
Adjacent sequences: A129815 A129816 A129817 this_sequence A129819 A129820 A129821
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KEYWORD
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sign,tabl,new
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 09 2007
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