A159667 - OEIS

%I #13 Sep 27 2022 02:27:16

%S 1,2,6,26,133,905,6521,57126,544820,5878219,66851119,881424550,

%T 11803494823,175906313032,2767829058956,47008174824136,

%U 821285150996811,15816596073011143,308160754687446289,6498330632792677804

%N For n >= 1, a(n) = A159666(n)/n.

%C a(n) is divisible by n, for all n >= 1.

%H G. C. Greubel, <a href="/A159667/b159667.txt">Table of n, a(n) for n = 1..445</a>

%t f[n_] := f[n] = Sum[Binomial[n, k] GCD[n, k] f[k - 1], {k, n}]; f[0] = 1; Table[f@n/n, {n, 22}] (* _Robert G. Wilson v_, May 27 2009 *)

%o (SageMath)

%o @CachedFunction

%o def b(n): return 1 if (n==0) else sum(binomial(n,j)*gcd(n,j)*b(j-1) for j in range(1,n+1)) # b = A159666

%o def A159667(n): return b(n)/n

%o [A159667(n) for n in range(1,40)] # _G. C. Greubel_, Sep 27 2022

%Y Cf. A159666.

%K nonn

%O 1,2

%A _Leroy Quet_, Apr 19 2009

%E More terms from _Robert G. Wilson v_, May 27 2009