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 A193822 Mirror of the triangle A193821. 4
 1, 1, 1, 3, 3, 2, 9, 9, 8, 4, 27, 27, 26, 20, 8, 81, 81, 80, 72, 48, 16, 243, 243, 242, 232, 192, 112, 32, 729, 729, 728, 716, 656, 496, 256, 64, 2187, 2187, 2186, 2172, 2088, 1808, 1248, 576, 128, 6561, 6561, 6560, 6544, 6432, 5984, 4864, 3072, 1280, 256 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A193822 is obtained by reversing the rows of the triangle A193821. LINKS FORMULA Write w(n,k) for the triangle at A193821.  The triangle at A193822 is then given by w(n,n-k). EXAMPLE First six rows: 1 1....1 3....3....2 9....9....8.....4 27...27...26....20...8 81...81...80....72...48...16 MATHEMATICA p[n_, x_] := (a*x + b)^n q[0, x_] := 1 q[n_, x_] := x*q[n - 1, x] + 1; q[n_, 0] := q[n, x] /. x -> 0; t[n_, k_] := Coefficient[p[n, x], x^k]; t[n_, 0] := p[n, x] /. x -> 0; w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1 g[n_] := CoefficientList[w[n, x], {x}] TableForm[Table[Reverse[g[n]], {n, -1, z}]] Flatten[Table[Reverse[g[n]], {n, -1, z}]]   (* A193821 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]]  (* A193822 *) CROSSREFS Cf. A193722, A193821. Sequence in context: A286952 A100052 A128504 * A202699 A058137 A250304 Adjacent sequences:  A193819 A193820 A193821 * A193823 A193824 A193825 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 06 2011 STATUS approved

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Last modified June 19 07:26 EDT 2021. Contains 345126 sequences. (Running on oeis4.)