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A157154 Triangle read by rows: A(n,0)=A(n,n)=1 and A(n,k)= (3*(n-k)+1)*A(n-1,k-1) + (3*k+1)*A(n-1,k) - 3*k*(n-k)*A(n-2,k-1), for 1<=k<n. 0

%I

%S 1,1,1,1,5,1,1,21,21,1,1,85,234,85,1,1,341,2110,2110,341,1,1,1365,

%T 17163,35882,17163,1365,1,1,5461,131751,505979,505979,131751,5461,1,1,

%U 21845,976876,6395471,11433118,6395471,976876,21845,1,1,87381,7089360

%N Triangle read by rows: A(n,0)=A(n,n)=1 and A(n,k)= (3*(n-k)+1)*A(n-1,k-1) + (3*k+1)*A(n-1,k) - 3*k*(n-k)*A(n-2,k-1), for 1<=k<n.

%C The row sums are 1, 2, 7, 44, 406, 4904, 72940, 1286384, 26221504, 606353744, 15680643352,...

%e 1;

%e 1, 1;

%e 1, 5, 1;

%e 1, 21, 21, 1;

%e 1, 85, 234, 85, 1;

%e 1, 341, 2110, 2110, 341, 1;

%e 1, 1365, 17163, 35882, 17163, 1365, 1;

%e 1, 5461, 131751, 505979, 505979, 131751, 5461, 1;

%e 1, 21845, 976876, 6395471, 11433118, 6395471, 976876, 21845, 1;

%e 1, 87381, 7089360, 75400800, 220599330, 220599330, 75400800, 7089360, 87381, 1;

%e 1, 349525, 50761485, 848430732, 3839932578, 6201694710, 3839932578, 848430732, 50761485, 349525, 1;

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

%t A[n_, 0, m_] := 1;

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

%t A[n_, k_, m_] := (m*(n - k) + 1)*A[n - 1, k - 1, m] + (m* k + 1)*A[n - 1, k, m] - m*k*(n - k)*A[n - 2, k - 1, m];

%t Table[A[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}];

%t Table[Flatten[Table[Table[A[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}]

%K nonn,tabl,easy

%O 0,5

%A _Roger L. Bagula_, Feb 24 2009

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)