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 A193093 Augmentation of the triangular array P=A094727 given by p(n,k)=n+k+1 for 0<=k<=n. See Comments. 3
 1, 2, 3, 6, 14, 19, 24, 72, 130, 169, 120, 432, 918, 1482, 1877, 720, 3000, 7224, 13140, 19846, 24675, 5040, 23760, 63600, 127104, 210726, 304006, 372611, 40320, 211680, 622080, 1350000, 2412408, 3754656, 5234114, 6340961, 362880, 2096640 (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, we have w(n,0)=(n+1)! . LINKS Table of n, a(n) for n=0..37. EXAMPLE First 5 rows: 1 2.....3 6.....14....19 24....72....130....169 120...432....918...1482...1877 MATHEMATICA p[n_, k_] := n + k + 1 Table[p[n, k], {n, 0, 5}, {k, 0, n}] (* A094727 *) 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}]] (* A193093 *) Flatten[Table[v[n], {n, 0, 8}]] CROSSREFS Cf. A094727. Sequence in context: A005537 A306600 A282351 * A182756 A152092 A187033 Adjacent sequences: A193090 A193091 A193092 * A193094 A193095 A193096 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jul 30 2011 STATUS approved

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Last modified August 11 07:13 EDT 2024. Contains 375059 sequences. (Running on oeis4.)