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 A209149 Triangle of coefficients of polynomials v(n,x) jointly generated with A209146; see the Formula section. 5
 1, 3, 1, 6, 5, 1, 12, 16, 7, 1, 24, 44, 30, 9, 1, 48, 112, 104, 48, 11, 1, 96, 272, 320, 200, 70, 13, 1, 192, 640, 912, 720, 340, 96, 15, 1, 384, 1472, 2464, 2352, 1400, 532, 126, 17, 1, 768, 3328, 6400, 7168, 5152, 2464, 784, 160, 19, 1, 1536, 7424 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Alternating row sums: 1,2,2,2,2,2,2,2,2,2,2,2,2,... For a discussion and guide to related arrays, see A208510. As triangle T(n,k) with 0<=k<=n, it is (3, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 08 2012 A skew triangle of A209144. - Philippe Deléham, Mar 08 2012 Riordan array ( (1 + x)/(1 - 2*x), x/(1 - 2*x) ). Cf. A118800. Matrix inverse is a signed version of A112626. - Peter Bala, Jul 17 2013 LINKS FORMULA u(n,x)=u(n-1,x)+(x+1)*v(n-1,x), v(n,x)=u(n-1,x)+(x+1)*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. As DELTA-triangle : T(n,k) = 2*T(n-1,k) + T(n-1,k-1), T(0,0) = 1, T(1,0) = 3, T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 08 2012 As DELTA-triangle : G.f. is (1+x)/(1-2*x-yx). - Philippe Deléham, Mar 08 2012 EXAMPLE First five rows: 1 3....1 6....5....1 12...16...7....1 24...44...30...9...1 First three polynomials v(n,x): 1, 3 + x, 6 + 5x + x^2. v(1,x) = 1 v(2,x) = 3 + x v(3,x) = (3 + x)*(2 + x) v(4,x) = (3 + x)*(2 + x)^2 v(5,x) = (3 + x)*(2 + x)^3 v(n,x) = (3 + x)*(2 + x)^(n-2)for n>1 . - Philippe Deléham, Mar 08 2012 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x]; v[n_, 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[%]    (* A209148 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A209149 *) CROSSREFS Cf. A209144, A209148, A208510. Sequence in context: A133545 A210214 A322427 * A210602 A210801 A153091 Adjacent sequences:  A209146 A209147 A209148 * A209150 A209151 A209152 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 07 2012 STATUS approved

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Last modified October 20 10:25 EDT 2019. Contains 328257 sequences. (Running on oeis4.)