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 A193980 Mirror of the triangle A193979. 2
 1, 3, 2, 9, 5, 3, 21, 13, 7, 4, 41, 28, 17, 9, 5, 71, 52, 35, 21, 11, 6, 113, 87, 63, 42, 25, 13, 7, 169, 135, 103, 74, 49, 29, 15, 8, 241, 198, 157, 119, 85, 56, 33, 17, 9, 331, 278, 227, 179, 135, 96, 63, 37, 19, 10, 441, 377, 315, 256, 201, 151, 107, 70, 41, 21, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A193980 is obtained by reversing the rows of the triangle A193977. LINKS Table of n, a(n) for n=0..65. FORMULA Write w(n,k) for the triangle at A193979. The triangle at A193980 is then given by w(n,n-k). EXAMPLE First six rows: 1 3....2 9....5....3 21...13...7....4 41...28...17...9....5 71...52...35...21...11...6 MATHEMATICA z = 11; p[0, x_] := 1; p[n_, x_] := x*p[n - 1, x] + n; q[n_, x_] := p[n, x]; 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}]] (* A193979 *) TableForm[Table[h[n], {n, 0, z}]] Flatten[Table[h[n], {n, -1, z}]] (* A193980 *) CROSSREFS Cf. A193979. Sequence in context: A258439 A346105 A188926 * A194001 A178230 A268824 Adjacent sequences: A193977 A193978 A193979 * A193981 A193982 A193983 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 10 2011 STATUS approved

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Last modified May 21 21:53 EDT 2024. Contains 372738 sequences. (Running on oeis4.)