A156534 - OEIS

%I #2 Mar 30 2012 17:34:33

%S 1,1,1,1,4,1,1,11,11,1,1,26,44,26,1,1,57,0,0,57,1,1,120,-1191,-6040,

%T -1191,120,1,1,247,-10017,-109333,-109333,-10017,247,1,1,502,-58432,

%U -1235276,-3061324,-1235276,-58432,502,1,1,1013,-287040,-10924608

%N A triangular recursion sequence: A(n,k,m)= (m* n - m*k + 1)*A(n - 1, k - 1, m) + (m*k - (m - 1))*A(n - 1, k, m); t(n,k)=2*A(n, k, 1)*A(n + 1, k + 1, 0)/(n - k + 1) - A(n, k, 0)*A(n, k, 1).

%C Row sums are:

%C {1, 2, 6, 24, 98, 116, -8180, -238204, -5647734, -132491004,...}.

%F A(n,k,m)= (m* n - m*k + 1)*A(n - 1, k - 1, m) + (m*k - (m - 1))*A(n - 1, k, m);

%F t(n,k)=2*A(n, k, 1)*A(n + 1, k + 1, 0)/(n - k + 1) - A(n, k, 0)*A(n, k, 1).

%e {1},

%e {1, 1},

%e {1, 4, 1},

%e {1, 11, 11, 1},

%e {1, 26, 44, 26, 1},

%e {1, 57, 0, 0, 57, 1},

%e {1, 120, -1191, -6040, -1191, 120, 1},

%e {1, 247, -10017, -109333, -109333, -10017, 247, 1},

%e {1, 502, -58432, -1235276, -3061324, -1235276, -58432, 502, 1},

%e {1, 1013, -287040, -10924608, -55034868, -55034868, -10924608, -287040, 1013, 1}

%t Clear[A, n, k, m, e];

%t A[n_, 1, m_] := 1; A[n_, n_, m_] := 1;

%t A[n_, k_, m_] := (m* n - m*k + 1)*A[n - 1, k - 1, m] + (m*k - (m - 1))*A[n - 1, k, m];

%t Table[Table[2*A[n, k, 1]*A[n + 1, k + 1, 0]/(n - k + 1) - A[n, k, 0]*A[n, k, 1], {k, 1, n}], {n, 10}];

%t Flatten[%]

%K sign,tabl,uned

%O 1,5

%A _Roger L. Bagula_, Feb 09 2009