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A086872
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Triangle T(n, k) read by rows; given by [1, 2, 3, 4, 5, 6, ..] DELTA [1, 4, 9, 16, 25, 36, ...] where DELTA is the operator defined in A084938.
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5
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1, 1, 1, 3, 8, 5, 15, 75, 121, 61, 105, 840, 2478, 3128, 1385, 945, 11025, 51030, 115350, 124921, 50521, 10395, 166320, 1105335, 3859680, 7365633, 7158128, 2702765
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| First column :1, 1, 3, 15, ... = A001147; double factorial numbers. Row sums : 1, 2, 16, 272, ...= A000182(n+1); tangent numbers. First diagonal : 1, 1, 5, 61, ... = A000364; Euler numbers. Sum( k>=0, T(n, k)*(-1)^k ) = 0; if n>0. Sum( k>=0, T(n, k)*(-1/2)^k ) = (1/2)^n.
Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = (-1)^n*A121822(n), (-1)^n*A092812(n), (-1)^n*A054879(n), A009117(n), A033999(n), A000007(n), A000364(n), A000182(n+1) for x = -6, -5, -4, -3, -2, -1, 0, 1 respectively .
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EXAMPLE
| Triangle begins:
1;
1, 1;
3, 8, 5;
15, 75, 121, 61;
105, 840, 2478, 3128, 1385;
945, 11025, 51030, 115350, 124921, 50521;
10395, 166320, 1105335, 3859680, 7365633, 7158128, 2702765 ; ...
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CROSSREFS
| Cf. A000182 A000364 A001147 A084938.
Sequence in context: A120070 A143753 A121164 * A054792 A144872 A090347
Adjacent sequences: A086869 A086870 A086871 * A086873 A086874 A086875
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Aug 20 2003, Aug 17 2007
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