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 A193847 Mirror of the triangle A193846. 4
 2, 8, 4, 26, 28, 8, 80, 136, 80, 16, 242, 568, 512, 208, 32, 728, 2188, 2672, 1648, 512, 64, 2186, 8020, 12392, 10288, 4832, 1216, 128, 6560, 28432, 53216, 55648, 35072, 13312, 2816, 256, 19682, 98416, 216512, 273376, 216512, 110080, 35072 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS A193847 is obtained by reversing the rows of the triangle A193846. LINKS FORMULA Write w(n,k) for the triangle at A193846.  The triangle at A193847 is then given by w(n,n-k). EXAMPLE First six rows: 2 8.....4 26....28....8 80....136...80....16 242...568...512...208...32 728...2188..2672..1648..512..64 MATHEMATICA p[n_, x_] := (x + 2)^n; q[n_, x_] := (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}]]   (* A193846 *) TableForm[Table[h[n], {n, 0, z}]] Flatten[Table[h[n], {n, -1, z}]]  (* A193847 *) TableForm[Table[Reverse[h[n]/2], {n, 0, z}]] Flatten[Table[Reverse[h[n]]/2, {n, -1, z}]] (* A193848 *) TableForm[Table[h[n]/2, {n, 0, z}]] Flatten[Table[h[n]/2, {n, -1, z}]]  (* A193849 *) CROSSREFS Cf. A193846, A193849. Sequence in context: A054788 A193851 A276624 * A019194 A038214 A195923 Adjacent sequences:  A193844 A193845 A193846 * A193848 A193849 A193850 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 07 2011 STATUS approved

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Last modified September 26 20:34 EDT 2021. Contains 347672 sequences. (Running on oeis4.)