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 A193998 Mirror of the triangle A193997. 2
 1, 3, 2, 6, 8, 3, 11, 23, 18, 5, 19, 55, 66, 37, 8, 32, 120, 196, 167, 73, 13, 53, 246, 511, 587, 388, 139, 21, 87, 484, 1225, 1777, 1578, 853, 259, 34, 142, 924, 2765, 4857, 5428, 3933, 1799, 474, 55, 231, 1725, 5969, 12333, 16642, 15147, 9275, 3678 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A193998 is obtained by reversing the rows of the triangle A193997. LINKS Table of n, a(n) for n=0..52. FORMULA Write w(n,k) for the triangle at A193997. The triangle at A193998 is then given by w(n,n-k). EXAMPLE First six rows: 1 3....2 6....8.....3 11...23....18....5 19...55....66....37....8 32...120...196...167...73...13 MATHEMATICA z = 11; p[n_, x_] := Sum[Fibonacci[k + 1]*x^(n - k), {k, 0, 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}]] (* A193997 *) TableForm[Table[h[n], {n, 0, z}]] Flatten[Table[h[n], {n, -1, z}]] (* A193998 *) CROSSREFS Cf. A193997. Sequence in context: A370665 A127717 A210236 * A209171 A368150 A348686 Adjacent sequences: A193995 A193996 A193997 * A193999 A194000 A194001 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 11 2011 STATUS approved

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Last modified May 21 15:47 EDT 2024. Contains 372738 sequences. (Running on oeis4.)