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A096421
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a(1)=1; for n>1, a(n) = sum{1<=j<n,GCD(j,n)=1} a(j) a(n-j).
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2
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1, 1, 2, 4, 12, 24, 88, 224, 720, 1792, 7200, 16512, 69952, 185984, 608896, 1797120, 7495424, 17936896, 79457792, 211576832, 742306816, 2190231552, 9482688512, 23198867456, 97967427584, 285227057152, 1046412681216, 3019819909120
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| a(1) = 1 & a(n)=sum([1/GCD(n, j)]a(j)a(n-j), {j=1..n-1}). - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 09 2004
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EXAMPLE
| Since 1 and 5 are the positive integers < 6 and coprime to 6, a(6) = a(1)a(5) + a(5)a(1) = 1*12 +12*1 = 24.
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MATHEMATICA
| a[1]=1; a[n_]:=a[n]=Sum[Floor[1/GCD[j, n]]a[j]a[n-j], {j, n-1}]; Table[a[n], {n, 30}] (Farideh Firoozbakht)
a[1] = 1; a[n_] := a[n] = Sum[ If[GCD[j, n] == 1, a[j]a[n - j], 0], {j, n - 1}]; Table[ a[n], {n, 28}] (from Robert G. Wilson v Aug 11 2004)
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PROG
| (PARI) {m=28; v=vector(m); v[1]=1; for(n=2, m, s=0; for(j=1, n-1, if(gcd(j, n)==1, s=s+v[j]*v[n-j])); v[n]=s); for(i=1, m, print1(v[i], ", "))} - Klaus Brockhaus, Aug 09 2004
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CROSSREFS
| Cf. A097365, A097366.
Sequence in context: A062177 A129643 A200337 * A066843 A051905 A051426
Adjacent sequences: A096418 A096419 A096420 * A096422 A096423 A096424
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Aug 08 2004
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EXTENSIONS
| More terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Robert G. Wilson v, Aug 09 2004
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