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 A193859 Mirror of the triangle A193858. 3
 1, 3, 2, 7, 10, 4, 15, 34, 28, 8, 31, 98, 124, 72, 16, 63, 258, 444, 392, 176, 32, 127, 642, 1404, 1672, 1136, 416, 64, 255, 1538, 4092, 6152, 5616, 3104, 960, 128, 511, 3586, 11260, 20488, 23536, 17440, 8128, 2176, 256, 1023, 8194, 29692, 63496 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A193859 is obtained by reversing the rows of the triangle A193858. LINKS FORMULA Write w(n,k) for the triangle at A193858.  The triangle at A193859 is then given by w(n,n-k). EXAMPLE First six rows: 1 3....2 7....10...4 15...34...28...8 31...98...124..72...16 63...258..444..392..176..32 MATHEMATICA z = 10; p[n_, x_] := (x + 1)^n; q[n_, x_] := (2 x + 1)^n; p1[n_, k_] := Coefficient[p[n, x], x^k]; p1[n_, 0] := p[n, x] /. x -> 0; d[n_, x_] := Sum[p1[n, k]*q[n - 1 - k, x], {k, 0, n - 1}] h[n_] := CoefficientList[d[n, x], {x}] TableForm[Table[Reverse[h[n]], {n, 0, z}]] Flatten[Table[Reverse[h[n]], {n, -1, z}]]  (* A193858 *) TableForm[Table[h[n], {n, 0, z}]] Flatten[Table[h[n], {n, -1, z}]]   (* A193859 *) CROSSREFS Cf. A193858. Sequence in context: A118966 A018891 A034423 * A174330 A099329 A182871 Adjacent sequences:  A193856 A193857 A193858 * A193860 A193861 A193862 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 07 2011 STATUS approved

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Last modified September 22 12:00 EDT 2021. Contains 347607 sequences. (Running on oeis4.)