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 A193920 Mirror of the triangle A193919. 2
 1, 1, 1, 2, 3, 1, 4, 9, 7, 2, 7, 21, 25, 14, 3, 12, 46, 75, 64, 28, 5, 20, 94, 195, 224, 148, 53, 8, 33, 185, 468, 679, 603, 326, 99, 13, 54, 353, 1056, 1855, 2073, 1502, 687, 181, 21, 88, 659, 2280, 4711, 6357, 5786, 3543, 1405, 327, 34, 143, 1209, 4755 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A193920 is obtained by reversing the rows of the triangle A193919. LINKS Table of n, a(n) for n=0..57. FORMULA Write w(n,k) for the triangle at A193919. The triangle at A193920 is then given by w(n,n-k). EXAMPLE First six rows: 1 1....1 2....3....1 4....9....7....2 7....21...25...14...3 12...46...75...64...28...5 MATHEMATICA p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, n}]; q[n_, x_] := (x + 1)^n; 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}]] (* A193919 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]] (* A193920 *) CROSSREFS Cf. A193919. Sequence in context: A165241 A119865 A177896 * A076732 A130152 A211233 Adjacent sequences: A193917 A193918 A193919 * A193921 A193922 A193923 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 09 2011 STATUS approved

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Last modified April 22 02:54 EDT 2024. Contains 371887 sequences. (Running on oeis4.)