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A161737
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Numerators of the column sums of the BG2 matrix.
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4
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2, 16, 128, 2048, 32768, 262144, 2097152, 67108864, 2147483648, 17179869184, 137438953472, 2199023255552, 35184372088832, 281474976710656, 2251799813685248, 144115188075855872, 9223372036854775808, 73786976294838206464, 590295810358705651712
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OFFSET
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2,1
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COMMENTS
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For the definition of the BG2 matrix coefficients see A161736.
This sequence can be linked with several other sequences, see the Maple programs.
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LINKS
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FORMULA
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a(n) = numer(sb(n)) with sb(n) = (2^(4*n-5)*(n-1)!^4)/((n-1)*(2*n-2)!^2) and A161736(n) = denom(sb(n)).
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EXAMPLE
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sb(2) = 2; sb(3) = 16/9; sb(4) = 128/75; sb(5) = 2048/1225; etc..
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MAPLE
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nmax := 18; with(Bits): A050605 := proc(a, b) option remember; if(0 = And(a, b)) then RETURN(0); else RETURN(1+A050605(Xor(a, b), 2*And(a, b))); fi; end: for n from 0 to nmax do y(n) := A050605(n, 2) od: x(2):=1: for n from 2 to nmax-1 do x(n+1) := y(n-2) + x(n) + 3 od: for n from 2 to nmax do a(n) := 2^x(n) od: seq(a(n), n=2..nmax);
# End program 1
nmax1 := nmax; A007814 := proc(n) local i, j; if n=0 then RETURN(0); fi; i:=0; j:=n; while j mod 2 <> 1 do i:=i+1; j:=j/2; od: i; end: for n from 0 to nmax1 do A090739(n) := A007814(n) + 3 od: for n from 0 to nmax1 do y(2*n+1) := A090739(n); y(2*n) := A090739(n) od: z(2) := 1: for n from 3 to nmax1 do z(n) := z(n-1) + y(n-1) od: for n from 2 to nmax1 do a(n) := 2^z(n) od: seq(a(n), n=2..nmax1);
# End program 2
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MATHEMATICA
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sb[2]=2; sb[n_] := sb[n] = sb[n-1]*4*(n-1)*(n-2)/(2n-3)^2; Table[sb[n] // Numerator, {n, 2, 20}] (* Jean-François Alcover, Aug 14 2017 *)
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PROG
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(PARI) vector(20, n, n++; numerator((2^(4*n-5)*(n-1)!^4)/((n-1)*(2*n-2)!^2))) \\ G. C. Greubel, Sep 26 2018
(Magma) [Numerator((2^(4*n-5)*(Factorial(n-1))^4)/((n-1)*(Factorial(2*n-2))^2)): n in [2..20]]; // G. C. Greubel, Sep 26 2018
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CROSSREFS
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KEYWORD
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easy,frac,nonn
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AUTHOR
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STATUS
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approved
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