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 A210555 Triangle of coefficients of polynomials u(n,x) jointly generated with A210556; see the Formula section. 2
 1, 1, 2, 1, 3, 4, 1, 4, 7, 8, 1, 5, 10, 17, 16, 1, 6, 13, 28, 39, 32, 1, 7, 16, 41, 70, 89, 64, 1, 8, 19, 56, 109, 176, 199, 128, 1, 9, 22, 73, 156, 297, 426, 441, 256, 1, 10, 25, 92, 211, 456, 765, 1020, 967, 512, 1, 11, 28, 113, 274, 657, 1236, 1953, 2398 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS 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)+1, 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 1...2 1...3...4 1...4...7....8 1...5...10...17...16 First three polynomials u(n,x): 1, 1 + 2x, 1 + 3x + 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] + 1; v[n_, x_] := x*u[n - 1, x] + (x + 1)*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[%]   (* A208341 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A210554 *) CROSSREFS Cf. A210554, A208510. Sequence in context: A132110 A039912 A163311 * A008949 A076832 A078925 Adjacent sequences:  A210552 A210553 A210554 * A210556 A210557 A210558 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 22 2012 STATUS approved

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Last modified November 21 07:01 EST 2017. Contains 294989 sequences.