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A193094
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Augmentation of the triangular array P=A130296 whose n-th row is (n+1,1,1,1,1...,1) for 0<=k<=n. See Comments.
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2
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1, 2, 1, 6, 4, 3, 24, 18, 16, 13, 120, 96, 90, 84, 71, 720, 600, 576, 558, 532, 461, 5040, 4320, 4200, 4128, 4050, 3908, 3447, 40320, 35280, 34560, 34200, 33888, 33462, 32540, 29093, 362880, 322560, 317520, 315360, 313800, 312096, 309330, 302436
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OFFSET
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0,2
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COMMENTS
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For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
diag (1,1,3,13,71,...): A003319, indecomposable permutations.
It appears that T(n,k) is the number of indecomposable permutations p of [n+2] for which p(k+2) = 1. For example, T(2,1) = 4 counts 2413, 3412, 4213, 4312. - David Callan, Aug 27 2014
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LINKS
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EXAMPLE
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First 5 rows:
1
2.....1
6.....4....3
24....18...16...13
120...96...90...84...71
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MATHEMATICA
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p[n_, k_] := If[k == 0, n + 1, 1]
Table[p[n, k], {n, 0, 5}, {k, 0, n}] (* A130296 *)
m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
TableForm[m[4]]
w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
v[n_] := v[n - 1].m[n]
TableForm[Table[v[n], {n, 0, 6}]] (* A193094 *)
Flatten[Table[v[n], {n, 0, 9}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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