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A062110
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Table read by antidiagonals where T(n,k) is coefficient of x^k in (1-x)^n/(1-2x)^n.
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7
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1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 4, 5, 3, 1, 0, 8, 12, 9, 4, 1, 0, 16, 28, 25, 14, 5, 1, 0, 32, 64, 66, 44, 20, 6, 1, 0, 64, 144, 168, 129, 70, 27, 7, 1, 0, 128, 320, 416, 360, 225, 104, 35, 8, 1, 0, 256, 704, 1008, 968, 681, 363, 147, 44, 9, 1, 0, 512, 1536, 2400, 2528, 1970
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Contribution from Paul Barry (pbarry(AT)wit.ie), Nov 10 2008: (Start)
As number triangle, Riordan array (1, x(1-x)/(1-2x)). A062110*A007318 is A147703.
[0,1,1,0,0,0,....] DELTA [1,0,0,0,.....] (Deleham DELTA defined in A084938). (End)
Modulo 2, this sequence becomes A106344 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 18 2008]
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FORMULA
| T(n, k)=T(n-1, k)+sum{j<k}[T(n, j)] with T(0, k)=0^k.
G.f.: 1/(1-x(1-y)/(1-2y)) = Sum_{i, j} a(i, j)x^i*y^j.
T(n,k)=A121462(n+1,k+1)*2^(n-2*k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 01 2006
Sum_{k, 0<=k<=n}T(n,k)*x^k = A152239(n), A152223(n), A152185(n), A152174(n), A152167(n), A152166(n), A152163(n), A000007(n), A001519(n), A006012(n), A081704(n), A082761(n), A147837(n), A147838(n), A147839(n), A147840(n), A147841(n), for x = -7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7,8,9 respectively. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 09 2008]
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EXAMPLE
| Rows start (1,0,0,0,0,...), (1,1,2,4,8,...), (1,2,5,12,28,...), etc.
Triangle begins : 1 ; 0, 1 ; 0, 1, 1 ; 0, 2, 2, 1 ; 0, 4, 5, 3, 1 ; 0, 8, 12, 9, 4, 1 ; 0, 16, 28, 25, 14, 5, 1 ; 0, 32, 64, 66, 44, 20, 6, 1 ; 0, 64, 144, 168, 129, 70, 27, 7, 1 ; 0, 128, 320, 416, 360, 225, 104, 35, 8, 1 ;... [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 30 2008]
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PROG
| (PARI) a(i, j)=if(i<0|j<0, 0, polcoeff(((1-x)/(1-2*x)+x*O(x^j))^i, j))
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CROSSREFS
| Rows include A000007, A011782, A045623, A058396, A062109, A169792, A169793, A169794, A169795, A169796, A169797.
Columns include A000012, A001477, A000096, A000297. Main diagonal is A002002. T(n, k) is a multiple of 2^(k-n), dividing by this gives a table similar to A050143 except at the edges.
Essentially the same array as A105306, A160232.
Sequence in context: A071510 A110124 A116389 * A122896 A191348 A198792
Adjacent sequences: A062107 A062108 A062109 * A062111 A062112 A062113
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KEYWORD
| nonn,tabl
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), May 30 2001
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