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 A193094 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. 2
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091. Regarding W=A193093: col 1: A000142, n! col 2: A001593, n*n! col 3: A130744, n*(n+2)*n! 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 LINKS Table of n, a(n) for n=0..43. EXAMPLE First 5 rows: 1 2.....1 6.....4....3 24....18...16...13 120...96...90...84...71 MATHEMATICA 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}]] CROSSREFS Cf. A193091, A130296, A193093. Sequence in context: A328923 A263271 A098697 * A021466 A286259 A257134 Adjacent sequences: A193091 A193092 A193093 * A193095 A193096 A193097 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jul 30 2011 STATUS approved

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Last modified August 8 08:46 EDT 2024. Contains 375018 sequences. (Running on oeis4.)