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 A208908 Triangle of coefficients of polynomials v(n,x) jointly generated with A208923; see the Formula section. 3
 1, 2, 2, 2, 5, 4, 2, 9, 15, 8, 2, 13, 33, 37, 16, 2, 17, 59, 103, 91, 32, 2, 21, 93, 221, 297, 213, 64, 2, 25, 135, 407, 739, 807, 491, 128, 2, 29, 185, 677, 1553, 2285, 2105, 1109, 256, 2, 33, 243, 1047, 2907, 5391, 6675, 5319, 2475, 512, 2, 37, 309, 1533 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Alternating row sums: 1,0,1,0,1,0,1,0,1,0,1,0,... For a discussion and guide to related arrays, see A208510. LINKS Table of n, a(n) for n=1..59. FORMULA u(n,x)=u(n-1,x)+2x*v(n-1,x), v(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 2...2 2...5....4 2...9...15...8 2...13...33...37...16 First five polynomials v(n,x): 1 2 + 2x 2 + 5x + 4x^2 2 + 9x + 15x^2 + 8x^3 2 + 13x + 33x^2 + 37x^3 + 16x^4 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x]; v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A208923 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%] (* A208908 *) CROSSREFS Cf. A208923, A208510. Sequence in context: A246119 A210562 A208512 * A209558 A209772 A370164 Adjacent sequences: A208905 A208906 A208907 * A208909 A208910 A208911 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 04 2012 STATUS approved

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Last modified August 14 02:14 EDT 2024. Contains 375146 sequences. (Running on oeis4.)