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 A193603 Augmentation of the triangle A008949.  See Comments. 1
 1, 1, 2, 1, 5, 8, 1, 9, 30, 44, 1, 14, 77, 212, 296, 1, 20, 163, 700, 1712, 2312, 1, 27, 305, 1877, 6882, 15476, 20384, 1, 35, 523, 4365, 22380, 73240, 154424, 199376, 1, 44, 840, 9134, 62479, 280630, 841312, 1683992, 2138336 (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.  The right edge of the triangle A193603 is A111537. LINKS EXAMPLE First five rows of A193603: 1 1...2 1...5....8 1...9...30....44 1...14...77..212...296 MATHEMATICA p[n_, k_] := Sum[Binomial[n, h], {h, 0, k}] (* A008949 *) Table[p[n, k], {n, 0, 5}, {k, 0, n}] 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}]] (* A193603 *) Flatten[Table[v[n], {n, 0, 8}]] CROSSREFS Cf. A008949, A193091, A111537. Sequence in context: A175770 A268950 A141507 * A059274 A082635 A166623 Adjacent sequences:  A193600 A193601 A193602 * A193604 A193605 A193606 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jul 31 2011 STATUS approved

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Last modified April 24 12:21 EDT 2019. Contains 322429 sequences. (Running on oeis4.)