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 A207612 Triangle of coefficients of polynomials u(n,x) jointly generated with A207613; see the Formula section. 3
 1, 2, 4, 2, 7, 6, 4, 12, 14, 12, 8, 20, 30, 32, 24, 16, 33, 60, 76, 72, 48, 32, 54, 116, 168, 184, 160, 96, 64, 88, 218, 356, 440, 432, 352, 192, 128, 143, 402, 728, 1000, 1104, 992, 768, 384, 256, 232, 730, 1452, 2184, 2656, 2688, 2240, 1664, 768, 512 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column 1:  A000071 Column 2:  2*A023610 LINKS FORMULA u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=u(n-1,x)+2x*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 2 4....2 7....6....4 12...14...12...8 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + v[n - 1, x] v[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x] + 1 Table[Factor[u[n, x]], {n, 1, z}] Table[Factor[v[n, x]], {n, 1, z}] cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; TableForm[cu] Flatten[%]    (* A207612 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A207613 *) PROG (Python) from sympy import Poly def u(n, x): return 1 if n==1 else u(n - 1, x) + v(n - 1, x) def v(n, x): return 1 if n==1 else u(n - 1, x) + 2*x*v(n - 1, x) + 1 def a(n): return Poly(u(n, x), x).all_coeffs()[::-1] for n in xrange(1, 13): print a(n) # Indranil Ghosh, May 28 2017 CROSSREFS Cf. A207613. Sequence in context: A110925 A214789 A207631 * A207620 A207622 A073017 Adjacent sequences:  A207609 A207610 A207611 * A207613 A207614 A207615 KEYWORD nonn,tabf AUTHOR Clark Kimberling, Feb 19 2012 STATUS approved

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Last modified October 20 07:23 EDT 2019. Contains 328252 sequences. (Running on oeis4.)