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 A208336 Triangle of coefficients of polynomials u(n,x) jointly generated with A208337; see the Formula section. 5
 1, 1, 1, 1, 2, 2, 1, 3, 5, 3, 1, 4, 9, 10, 5, 1, 5, 14, 22, 20, 8, 1, 6, 20, 40, 51, 38, 13, 1, 7, 27, 65, 105, 111, 71, 21, 1, 8, 35, 98, 190, 256, 233, 130, 34, 1, 9, 44, 140, 315, 511, 594, 474, 235, 55, 1, 10, 54, 192, 490, 924, 1295, 1324, 942, 420, 89, 1, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS coef. of x^(n-1) in u(n,x): A000045(n), Fibonacci numbers coef. of x^(n-1) in v(n,x): A000045(n+1) row sums, u(n,1):  A000129 row sums, v(n,1):  A001333 alternating row sums, u(n,-1): 1,0,1,0,1,0,1,0,1,0,... alternating row sums, v(n,-1): 1,-1,1,-1,1,-1,1,-1,... LINKS FORMULA u(n,x)=u(n-1,x)+x*v(n-1,x), v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x), where u(1,x)=1, v(1,x)=1. T(n,k) = A038137(n-1,k). - Philippe Deléham, Apr 05 2012 EXAMPLE First five rows: 1 1...1 1...2...2 1...3...5...3 1...4...9...10...5 First five polynomials u(n,x): 1 1 + x 1 + 2x + 2x^2 1 + 3x + 5x^2 + 3x^3 1 + 4x + 9x^2 + 10x^3 + 5x^4 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 13; u[n_, x_] := u[n - 1, x] + x*v[n - 1, x]; v[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x]; 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[%]    (* A208336 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A208337 *) Table[u[n, x] /. x -> 1, {n, 1, z}] (* u row sums *) Table[v[n, x] /. x -> 1, {n, 1, z}] (* v row sums *) Table[u[n, x] /. x -> -1, {n, 1, z}](* u alt. row sums *) Table[v[n, x] /. x -> -1, {n, 1, z}](* v alt. row sums *) CROSSREFS Cf. A038137, A208337. Sequence in context: A239830 A140767 A060850 * A038137 A073133 A106179 Adjacent sequences:  A208333 A208334 A208335 * A208337 A208338 A208339 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Feb 26 2012 STATUS approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)