A159667 For n >= 1, a(n) = A159666(n)/n.

1, 2, 6, 26, 133, 905, 6521, 57126, 544820, 5878219, 66851119, 881424550, 11803494823, 175906313032, 2767829058956, 47008174824136, 821285150996811, 15816596073011143, 308160754687446289, 6498330632792677804

Offset

1,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..445

Mathematica

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 *)

Prog

(SageMath)
@CachedFunction
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
def A159667(n): return b(n)/n
[A159667(n) for n in range(1, 40)] # G. C. Greubel, Sep 27 2022

Crossrefs

Cf. A159666.

Sequence in context: A030850 A030951 A030876 * A370215 A326562 A030957

Adjacent sequences: A159664 A159665 A159666 * A159668 A159669 A159670

Keyword

nonn

Author

Leroy Quet, Apr 19 2009

Extensions

More terms from Robert G. Wilson v, May 27 2009

Status

approved