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 A209692 Triangle of coefficients of polynomials v(n,x) jointly generated with A209691; see the Formula section. 3
 1, 2, 2, 1, 6, 4, 1, 4, 16, 8, 1, 3, 16, 40, 16, 1, 3, 11, 56, 96, 32, 1, 3, 10, 43, 176, 224, 64, 1, 3, 10, 35, 163, 512, 512, 128, 1, 3, 10, 34, 128, 579, 1408, 1152, 256, 1, 3, 10, 34, 117, 477, 1923, 3712, 2560, 512, 1, 3, 10, 34 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Combinatorial limit of rows:  A007052. 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)=v(1,x)=1. EXAMPLE First five rows: 1 2...2 1...6...4 1...4...16...8 1...3...16...40...16 First three polynomials v(n,x): 1, 2 + 2x , 1 + 6x + 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. A209691, A208510. Sequence in context: A290013 A220963 A179313 * A178886 A065052 A128308 Adjacent sequences:  A209689 A209690 A209691 * A209693 A209694 A209695 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 12 2012 STATUS approved

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Last modified October 18 00:09 EDT 2019. Contains 328135 sequences. (Running on oeis4.)