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 A193606 Augmentation of the triangle A193605.  See Comments. 2
 1, 1, 3, 1, 7, 17, 1, 12, 57, 127, 1, 18, 134, 531, 1125, 1, 25, 265, 1556, 5513, 11279, 1, 33, 470, 3793, 19152, 62675, 124837, 1, 42, 772, 8175, 55297, 250524, 771121, 1502679, 1, 52, 1197, 16087, 140269, 834879, 3478204, 10185019, 19480445 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091. LINKS EXAMPLE First five rows of A193606: 1 1...3 1...7....17 1...12...57....127 1...18...134...531...1125 MATHEMATICA u[n_, k_] := Sum[Binomial[n, h], {h, 0, k}] p[n_, k_] := Sum[u[n, h], {h, 0, k}] Table[p[n, k], {n, 0, 12}, {k, 0, n}] (* A193695 *) 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}]] (* A193606 *) Flatten[Table[v[n], {n, 0, 8}]] CROSSREFS Cf. A193605, A193091. Sequence in context: A232295 A228763 A101845 * A221328 A280610 A280416 Adjacent sequences:  A193603 A193604 A193605 * A193607 A193608 A193609 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jul 31 2011 STATUS approved

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Last modified May 24 18:25 EDT 2022. Contains 354043 sequences. (Running on oeis4.)