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 A193819 Mirror of the triangle A193818. 2
 1, 1, 2, 2, 6, 4, 3, 12, 16, 8, 4, 20, 40, 40, 16, 5, 30, 80, 120, 96, 32, 6, 42, 140, 280, 336, 224, 64, 7, 56, 224, 560, 896, 896, 512, 128, 8, 72, 336, 1008, 2016, 2688, 2304, 1152, 256, 9, 90, 480, 1680, 4032, 6720, 7680, 5760, 2560, 512, 10, 110, 660 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A193819 is obtained by reversing the rows of the triangle A193818. LINKS FORMULA Write w(n,k) for the triangle at A193818.  The triangle at A193819 is then given by w(n,n-k). Triangle T(n,k), read by rows, given by (1,1,-1,1,0,0,0,0,0,0,0,...) DELTA (2,0,-2,2,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - From Philippe Deléham, Oct 05 2011. T(n,k)=A153861(n,k)*2^k. - From Philippe Deléham, Oct 09 2011. EXAMPLE First six rows: 1 1....2 2....6....4 3....12...16....8 4....20...40....40...16 5....30...80....120..96...32 MATHEMATICA z = 10; c = 2; d = 1; p[0, x_] := 1 p[n_, x_] := x*p[n - 1, x] + 1; p[n_, 0] := p[n, x] /. x -> 0; q[n_, x_] := (c*x + d)^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}]]  (* A193818 *) TableForm[Table[g[n], {n, -1, z}]] Flatten[Table[g[n], {n, -1, z}]]   (* A193819 *) CROSSREFS Cf. A084938, A193722, A193818. Sequence in context: A137316 A064851 A134458 * A182786 A009279 A059943 Adjacent sequences:  A193816 A193817 A193818 * A193820 A193821 A193822 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Aug 06 2011 STATUS approved

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Last modified May 25 21:30 EDT 2013. Contains 225649 sequences.