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 A210561 Triangle of coefficients of polynomials u(n,x) jointly generated with A210562; see the Formula section. 2
 1, 1, 2, 1, 3, 4, 1, 3, 8, 8, 1, 3, 9, 20, 16, 1, 3, 9, 26, 48, 32, 1, 3, 9, 27, 72, 112, 64, 1, 3, 9, 27, 80, 192, 256, 128, 1, 3, 9, 27, 81, 232, 496, 576, 256, 1, 3, 9, 27, 81, 242, 656, 1248, 1280, 512, 1, 3, 9, 27, 81, 243, 716, 1808, 3072, 2816, 1024, 1, 3, 9 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Last term in row n:  2^(n-1) Limiting row:  3^(k-1) 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)=(x+1)*u(n-1,x)+x*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. From Peter Bala, Mar 06 2017: (Start) T(n,k) = 2*T(n-1,k-1) + T(n-2,k-1). E.g.f. for n-th subdiagonal: exp(2*x)*(1 + x + x^2/2! + x^3/3! + ... + x^n/n!). Cf. A004070. Riordan array (1/(1 - x), x*(2 + x)). Row sums A048739. (End) EXAMPLE First five rows: 1 1...2 1...3...4 1...3...8...8 1...3...9...20...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 + 1)*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[%]  (* A210559 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]  (* A210560 *) CROSSREFS Cf. A210562, A208510, A004070, A048739. Sequence in context: A186975 A027422 A135086 * A210549 A187002 A177226 Adjacent sequences:  A210558 A210559 A210560 * A210562 A210563 A210564 KEYWORD nonn,tabl,easy AUTHOR Clark Kimberling, Mar 22 2012 STATUS approved

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Last modified October 22 03:04 EDT 2019. Contains 328315 sequences. (Running on oeis4.)