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A188587
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1-Euler triangle.
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3
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1, 1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 14, 30, 14, 1, 1, 33, 146, 146, 33, 1, 1, 72, 603, 1168, 603, 72, 1, 1, 151, 2241, 7687, 7687, 2241, 151, 1, 1, 310, 7780, 44194, 76870, 44194, 7780, 310, 1, 1, 629, 25820, 231236, 649514, 649514, 231236, 25820, 629, 1, 1, 1268, 83121, 1131504, 4866222, 7794168, 4866222, 1131504, 83121, 1268, 1
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table;
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refs;
listen;
history;
text;
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OFFSET
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0,8
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COMMENTS
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Formed with the same recurrence as the Euler triangle A008292 (adjusted for offset), but with the middle element of row n=2 set to 1.
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LINKS
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FORMULA
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T(n,k) = 0 if k < 0 or k > n.
T(n,k) = 1 if k=0 or k=n or n=2.
T(n,k)= (n-k+1)*T(n-1,k-1) + (k+1)*T(n-1,k), n > 2 and 1 <= k < n.
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EXAMPLE
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Triangle begins
1;
1, 1;
1, 1, 1;
1, 5, 5, 1;
1, 14, 30, 14, 1;
1, 33, 146, 146, 33, 1;
1, 72, 603, 1168, 603, 72, 1;
1, 151, 2241, 7687, 7687, 2241, 151, 1;
1, 310, 7780, 44194, 76870, 44194, 7780, 310, 1;
1, 629, 25820, 231236, 649514, 649514, 231236, 25820, 629, 1;
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MAPLE
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A188587 := proc(n, k) if k < 0 or k > n then 0; elif k=0 or k= n or n=2 then 1; else (n-k+1)*procname(n-1, k-1)+(k+1)*procname(n-1, k) ; end if; end proc:
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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