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A154698
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Triangular sequence T(n, m) = (p^(n-m)*q^m + p^m*q^(n-m))*A(n+1, m+1), where A(n, m) = (3*n -3*k +1)A(n-1, k-1) + (3*k-2)A(n-1, k), A(n,1)=A(n,n)=1, p=2 and q=3.
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1
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2, 5, 5, 13, 96, 13, 35, 1170, 1170, 35, 97, 12948, 39312, 12948, 97, 275, 142170, 986760, 986760, 142170, 275, 793, 1585368, 22077900, 47364480, 22077900, 1585368, 793, 2315, 18009750, 470999340, 1846449000, 1846449000, 470999340, 18009750, 2315
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OFFSET
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0,1
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LINKS
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EXAMPLE
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Triangle begins as:
2;
5, 5;
13, 96, 13;
35, 1170, 1170, 35;
97, 12948, 39312, 12948, 97;
275, 142170, 986760, 986760, 142170, 275;
793, 1585368, 22077900, 47364480, 22077900, 1585368, 793;
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MATHEMATICA
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p=2; q=3;
A[n_, 1]:= 1; A[n_, n_]:= 1; A[n_, k_]:= (3*n-3*k+1)*A[n-1, k-1] + (3*k-2)*A[n-1, k];
T[n_, m_] := (p^(n-m)*q^m + p^m*q^(n-m)) *A[n+1, m+1];
Table[T[n, m], {n, 0, 10}, {m, 0, n}]//Flatten (* modified by G. C. Greubel, May 08 2019 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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