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A156188 Triangle: m=5; e(n,k,n)=(k + m - 1)*e(n - 1, k, m) + (m*n - k + 1 - m)*e(n - 1, k - 1, m); t(n,k)=e(n,k,m)+e(n,n-k,m).

%I A156188 #7 Feb 18 2024 09:10:35
%S A156188 2,1,1,1,10,1,1,80,80,1,1,775,1520,775,1,1,10915,25945,25945,10915,1,
%T A156188 1,213720,542910,624670,542910,213720,1,1,5245530,14690640,16408670,
%U A156188 16408670,14690640,5245530,1,1,151534685,479956020,553630850,464654480
%N A156188 Triangle: m=5; e(n,k,n)=(k + m - 1)*e(n - 1, k, m) + (m*n - k + 1 - m)*e(n - 1, k - 1, m); t(n,k)=e(n,k,m)+e(n,n-k,m).
%F A156188 m=5; e(n,k,n) = (k + m - 1)*e(n - 1, k, m) + (m*n - k + 1 - m)*e(n - 1, k - 1, m);
%F A156188 t(n,k) = e(n,k,m) + e(n,n-k,m).
%e A156188 {2},
%e A156188 {1, 1},
%e A156188 {1, 10, 1},
%e A156188 {1, 80, 80, 1},
%e A156188 {1, 775, 1520, 775, 1},
%e A156188 {1, 10915, 25945, 25945, 10915, 1},
%e A156188 {1, 213720, 542910, 624670, 542910, 213720, 1},
%e A156188 {1, 5245530, 14690640, 16408670, 16408670, 14690640, 5245530, 1},...
%t A156188 m = 5; e[n_, 0, m_] := 1;
%t A156188 e[n_, k_, m_] := 0 /; k >= n;
%t A156188 e[n_, k_, 1] := 1 /; k >= n;
%t A156188 e[n_, k_, m_] := (k + m - 1)e[n - 1, k, m] + (m*n - k + 1 - m)e[n - 1, k - 1, m];
%t A156188 Table[Table[e[n, k, m], {k, 0, n - 1}], {n, 1, 10}];
%t A156188 Table[Table[e[n, k, m] + e[n, n - k, m], {k, 0, n}], {n, 0, 10}];
%t A156188 Flatten[%]
%Y A156188 Cf. A054091, A054090, A008517, A156141.
%K A156188 nonn,tabl,uned
%O A156188 0,1
%A A156188 _Roger L. Bagula_, Feb 05 2009