%I A156534
%S A156534 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 A156534 1191,120,1,1,247,10017,109333,109333,10017,247,1,1,502,58432,
%U A156534 1235276,3061324,1235276,58432,502,1,1,1013,287040,10924608
%V A156534 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,
%W A156534 -1191,120,1,1,247,-10017,-109333,-109333,-10017,247,1,1,502,-58432,
%X A156534 -1235276,-3061324,-1235276,-58432,502,1,1,1013,-287040,-10924608
%N A156534 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 A156534 Row sums are:
%C A156534 {1, 2, 6, 24, 98, 116, -8180, -238204, -5647734, -132491004,...}.
%F A156534 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 A156534 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 A156534 {1},
%e A156534 {1, 1},
%e A156534 {1, 4, 1},
%e A156534 {1, 11, 11, 1},
%e A156534 {1, 26, 44, 26, 1},
%e A156534 {1, 57, 0, 0, 57, 1},
%e A156534 {1, 120, -1191, -6040, -1191, 120, 1},
%e A156534 {1, 247, -10017, -109333, -109333, -10017, 247, 1},
%e A156534 {1, 502, -58432, -1235276, -3061324, -1235276, -58432, 502, 1},
%e A156534 {1, 1013, -287040, -10924608, -55034868, -55034868, -10924608, -287040, 
               1013, 1}
%t A156534 Clear[A, n, k, m, e];
%t A156534 A[n_, 1, m_] := 1; A[n_, n_, m_] := 1;
%t A156534 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 A156534 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 A156534 Flatten[%]
%Y A156534 Sequence in context: A152970 A154986 A154983 this_sequence A008292 A157221 
               A146967
%Y A156534 Adjacent sequences: A156531 A156532 A156533 this_sequence A156535 A156536 
               A156537
%K A156534 sign,tabl,uned
%O A156534 1,5
%A A156534 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 09 2009