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%I #2 Mar 30 2012 17:34:28
%S 2,3,3,2,14,2,2,25,25,2,2,46,66,46,2,2,88,207,207,88,2,2,172,693,1128,
%T 693,172,2,2,340,2319,6114,6114,2319,340,2,2,676,7617,31440,49860,
%U 31440,7617,676,2,2,1348,24519,153570,370686,370686,153570,24519,1348,2
%N Recursive triangular symmetrical sequence: A(n,k) := (n - k + 1)A(n - 1, k - 1) + (k)* A(n - 1, k) - (n + 1)*A(n - 2, k - 1).
%C Row sums are:
%C {2, 6, 18, 54, 162, 594, 2862, 17550, 129330, 1100250,...}
%F A(n,k) := (n - k + 1)A(n - 1, k - 1) + (k)* A(n - 1, k) - (n + 1)*A(n - 2, k - 1).
%e {2},
%e {3, 3},
%e {2, 14, 2},
%e {2, 25, 25, 2},
%e {2, 46, 66, 46, 2},
%e {2, 88, 207, 207, 88, 2},
%e {2, 172, 693, 1128, 693, 172, 2},
%e {2, 340, 2319, 6114, 6114, 2319, 340, 2},
%e {2, 676, 7617, 31440, 49860, 31440, 7617, 676, 2},
%e {2, 1348, 24519, 153570, 370686, 370686, 153570, 24519, 1348, 2}
%t Clear[t, n, m, A];
%t A[2, 1] := A[2, 2] = 3;
%t A[3, 2] = 14; A[4, 2] = 25; A[4, 3] = 25;
%t A[n_, 1] := 2;A[n_, n_] := 2
%t A[n_, k_] := (n - k + 1)A[n - 1, k - 1] + (k)* A[n - 1,k] - (n + 1)*A[n - 2, k - 1];
%t Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}]
%t Flatten[%]
%K nonn,uned,tabl
%O 0,1
%A _Roger L. Bagula_, Dec 27 2008
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