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 A209691 Triangle of coefficients of polynomials u(n,x) jointly generated with A209692; see the Formula section. 3
 1, 0, 2, 0, 2, 4, 0, 1, 8, 8, 0, 1, 5, 24, 16, 0, 1, 4, 21, 64, 32, 0, 1, 4, 15, 77, 160, 64, 0, 1, 4, 14, 58, 253, 384, 128, 0, 1, 4, 14, 49, 221, 765, 896, 256, 0, 1, 4, 14, 48, 177, 800, 2173, 2048, 512, 0, 1, 4, 14, 48, 165, 654, 2723, 5885, 4608, 1024, 0, 1, 4 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Combinatorial limit of rows:  A007070. For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+x*v(n-1,x), v(n,x)=u(n-1,x)+2x*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 0...2 0...2...4 0...1...8...8 0...1...5...24...16 First three polynomials v(n,x): 1, 2x, 2x + 4x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x]; v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1; Table[Expand[u[n, x]], {n, 1, z/2}] Table[Expand[v[n, x]], {n, 1, z/2}] cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; TableForm[cu] Flatten[%]   (* A209691 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A209692 *) CROSSREFS Cf. A209692, A208510. Sequence in context: A136716 A117946 A061930 * A221683 A199335 A141660 Adjacent sequences:  A209688 A209689 A209690 * A209692 A209693 A209694 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 12 2012 STATUS approved

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Last modified October 22 18:44 EDT 2019. Contains 328319 sequences. (Running on oeis4.)