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 A209561 Triangle of coefficients of polynomials u(n,x) jointly generated with A209562; see the Formula section. 6
 1, 1, 1, 2, 2, 1, 3, 4, 3, 1, 4, 7, 7, 4, 1, 5, 11, 14, 11, 5, 1, 6, 16, 25, 25, 16, 6, 1, 7, 22, 41, 50, 41, 22, 7, 1, 8, 29, 63, 91, 91, 63, 29, 8, 1, 9, 37, 92, 154, 182, 154, 92, 37, 9, 1, 10, 46, 129, 246, 336, 336, 246, 129, 46, 10, 1, 11, 56, 175, 375, 582, 672 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Alternating row sums: 1,0,1,1,1,1,1,1,1,1,1,1,1,1,... For a discussion and guide to related arrays, see A208510. LINKS Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened FORMULA u(n,x)=x*u(n-1,x)+v(n-1,x), v(n,x)=x*u(n-1,x)+v(n-1,x) +1, where u(1,x)=1, v(1,x)=1. T(n,n) = 1; T(n,k) = A051597(n-2,k-1), 1 <= k < n. - Reinhard Zumkeller, Dec 26 2012 EXAMPLE First five rows: 1 1...1 2...2...1 3...4...3...1 4...7...7...4...1 First three polynomials v(n,x): 1, 1 + x, 2 + 2x + x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x]; v[n_, x_] := x*u[n - 1, 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[%]   (* A209561 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A209562 *) PROG (Haskell) a209561 n k = a209561_tabl !! (n-1) !! (k-1) a209561_row n = a209561_tabl !! (n-1) a209561_tabl = [1] : iterate                (\row -> zipWith (+) ([1] ++ row) (row ++ [0])) [1, 1] -- Reinhard Zumkeller, Dec 26 2012 CROSSREFS Cf. A209562, A208510. Cf. A083329 (row sums), A097613 (central terms). Sequence in context: A208805 A208514 A179901 * A283822 A210789 A105809 Adjacent sequences:  A209558 A209559 A209560 * A209562 A209563 A209564 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 10 2012 STATUS approved

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Last modified October 22 17:54 EDT 2019. Contains 328319 sequences. (Running on oeis4.)