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Search: id:A088996
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| A088996 |
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Triangle T(n,k) read by rows, given by [0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, ...] DELTA [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, ...] where DELTA is the operator defined in A084938. |
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2
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| 1, 0, 1, 0, 1, 2, 0, 2, 7, 6, 0, 6, 29, 46, 24, 0, 24, 146, 329, 326, 120, 0, 120, 874, 2521, 3604, 2556, 720, 0, 720, 6084, 21244, 39271, 40564, 22212, 5040, 0, 5040, 48348, 197380, 444849, 598116, 479996, 212976, 40320
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Diagonals give A000007, A000142; A000142, A067318 . Row sums : A001147 . Sum(k=0..n, (-1)^k*T(n,k))= (-1)^n.
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FORMULA
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E.g.f.: (1-y-y*x)^(-1/(1+x)). Sum(k=0..n, T(n, k)*x^k) = Product(k=1..n, k*x+k-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 15 2004
T(n, k) = n*T(n-1, k-1) + (n-1)*T(n-1, k); T(0, 0) = 1, T(0, k) = 0 if k>0, T(n, k) = 0 if k<0. - Philippe DELEHAM, May 22 2005
Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A019590(n+1), A000012(n), A000142(n), A001147(n), A007559(n), A007696(n), A008548(n), A008542(n), A045754(n), A045755(n) for x= -2, -1, 0, 1, 2, 3, 4, 5, 6, 7 respectively . Sum_{k, 0<=k<=n}T(n,k)*x^k = A033999(n), A000007(n), A001147(n), A008544(n), A008545(n), A008546(n), A008543(n), A049209(n), A049210(n), A049211(n), A049212(n) for x= -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 respectively . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Aug 10 2007
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 1, 2;
0, 2, 7, 6;
0, 6, 29, 46, 24;
0, 24, 146, 329, 326, 120;
0, 120, 874, 2521, 3604, 2556, 720;
0, 720, 6084, 21244, 39271, 40564, 22212, 5040;
0, 5040, 48348, 197380, 444849, 598116, 479996, 212976, 40320;
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CROSSREFS
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Cf. A000007 A000142 A001147 A067318 A084938.
Adjacent sequences: A088993 A088994 A088995 this_sequence A088997 A088998 A088999
Sequence in context: A111111 A161014 A154852 this_sequence A021497 A029593 A004514
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 01 2003, Aug 17 2007
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