A096421 a(1)=1; for n > 1, a(n) = Sum_{1<=j<n, gcd(j,n)=1} a(j)*a(n-j).

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

Offset

1,3

Links

Table of n, a(n) for n=1..28.

Formula

a(1) = 1, a(n) = Sum_{j=1..n-1} (1/gcd(n, j))*a(j)*a(n-j), {}). - Farideh Firoozbakht, Aug 09 2004

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.

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, Aug 09 2004 *)
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}] (* Robert G. Wilson v, Aug 11 2004 *)

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

Crossrefs

Cf. A097365, A097366.

Sequence in context: A367173 A367703 A320931 * A066843 A051905 A051426

Adjacent sequences: A096418 A096419 A096420 * A096422 A096423 A096424

Keyword

nonn

Author

Leroy Quet, Aug 08 2004

Extensions

More terms from Farideh Firoozbakht, Klaus Brockhaus and Robert G. Wilson v, Aug 09 2004

Status

approved