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 A209570 Triangle of coefficients of polynomials v(n,x) jointly generated with A209569; see the Formula section. 3
 1, 2, 2, 3, 4, 2, 4, 8, 8, 2, 5, 14, 20, 12, 2, 6, 22, 42, 40, 16, 2, 7, 32, 78, 102, 68, 20, 2, 8, 44, 132, 222, 210, 104, 24, 2, 9, 58, 208, 432, 534, 382, 148, 28, 2, 10, 74, 310, 772, 1188, 1126, 634, 200, 32, 2, 11, 92, 442, 1290, 2392, 2848, 2142, 982 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n>1, row n begins and ends with 2. Alternating row sums:  1,0,1,2,1,0,1,2,1,0,1,2,... For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+v(n-1,x), v(n,x)=2x*u(n-1,x)+v(n-1,x) +1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 2...2 3...4....2 4...8....8....2 5...14...20...12...2 First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 2x^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_] := 2 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[%]   (* A209569 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A209570 *) CROSSREFS Cf. A209569, A208510. Sequence in context: A143595 A211702 A208521 * A205703 A325785 A207632 Adjacent sequences:  A209567 A209568 A209569 * A209571 A209572 A209573 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 10 2012 STATUS approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)