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A161737
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Numerators of the column sums of the BG2 matrix
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3
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2, 16, 128, 2048, 32768, 262144, 2097152, 67108864, 2147483648, 17179869184, 137438953472, 2199023255552, 35184372088832, 281474976710656, 2251799813685248, 144115188075855872, 9223372036854775808
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| 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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FORMULA
| 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
| sb(2) = 2; sb(3) = 16/9; sb(4) = 128/75; sb(5) = 2048/1225; etc..
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MAPLE
| restart; nmax:=19; 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);
restart; nmax:=19; 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 nmax do A090739(n):=A007814(n)+3 od: for n from 0 to nmax do y(2*n+1):=A090739(n); y(2*n):=A090739(n) od: z(2):=1: for n from 3 to nmax do z(n):=z(n-1)+y(n-1) od: for n from 2 to nmax do a(n):=2^z(n) od: seq(a(n), n=2..nmax);
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CROSSREFS
| Cf. A161736 and A161738.
Cf. A050605, A007814 and A090739.
Sequence in context: A069868 A022027 A013730 * A171451 A012459 A012463
Adjacent sequences: A161734 A161735 A161736 * A161738 A161739 A161740
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KEYWORD
| easy,frac,nonn
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AUTHOR
| Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 18 2009
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