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A128908
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Riordan array (1,x/(1-x)^2).
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5
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1, 0, 1, 0, 2, 1, 0, 3, 4, 1, 0, 4, 10, 6, 1, 0, 5, 20, 21, 8, 1, 0, 6, 35, 56, 36, 10, 1, 0, 7, 56, 126, 120, 55, 12, 1, 0, 8, 84, 252, 330, 220, 78, 14, 1, 0, 9, 120, 462, 792, 715, 364, 105, 16, 1, 0, 10, 165, 792, 1716, 2002, 1365, 560, 136, 18, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Triangle T(n,k), 0<=k<=n, read by rows given by [0,2,-1/2,1/2,0,0,0,0,0,...] DELTA [1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 .
Row sums give A088305 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007
Column k is C(n,2k-1) for k>0. - DELEHAM Philippe, Jan 20 2012
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FORMULA
| T(n,0)=0^n, T(n,k)=binomial(n+k-1,2k-1) for k>=1 .
Sum_{k, 0<=k<=n}T(n,k)*2^(n-k)= A002450(n)=(4^n-1)/3 for n>=1 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 19 2008]
G.f.: (1-x)^2/(1-(2+y)*x+x^2) - DELEHAM Philippe, Jan 20 2012
Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n*A001352(n), (-1)^(n+1)*A054888(n+1), (-1)^n*A008574(n), (-1)^n*A084103(n), (-1)^n*A084099(n), A163810(n), A000007(n), A088305(n) for x = -6, -5, -4, -3, -2, -1, 0, 1 respectively. - DELEHAM Philippe, Jan 20 2012
Riordan array (1, x/(1-x)^2). - DELEHAM Philippe, Jan 20 2012
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EXAMPLE
| Triangle begins:
1;
0, 1;
0, 2, 1;
0, 3, 4, 1;
0, 4, 10, 6, 1;
0, 5, 20, 21, 8, 1;
0, 6, 35, 56, 36, 10, 1;
0, 7, 56, 126, 120, 55, 12, 1;
0, 8, 84, 252, 330, 220, 78, 14, 1;
0, 9, 120, 462, 792, 715, 364, 105, 16, 1;
0, 10, 165, 792, 1716, 2002, 1365, 560, 136, 18, 1 ;...
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CROSSREFS
| Cf. A007318, A078812, A034008.
Cf. Columns : A000007, A000027, A000292, A000389, A000580, A000582, A001288, A010966 ..(+2).. A011000, A017713 ..(+2).. A017763
Sequence in context: A108887 A193401 A095884 * A155112 A188286 A101603
Adjacent sequences: A128905 A128906 A128907 * A128909 A128910 A128911
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 22 2007
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