A159666 a(n) = Sum_{k=1..n} binomial(n,k) * gcd(n,k) * a(k-1), with a(0) = 1.

1, 1, 4, 18, 104, 665, 5430, 45647, 457008, 4903380, 58782190, 735362309, 10577094600, 153445432699, 2462688382448, 41517435884340, 752130797186176, 13961847566945787, 284698729314200574, 5855054339061479491

Offset

0,3

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..445

Mathematica

a[n_]:= a[n] = If[n==0, 1, Sum[Binomial[n, k] GCD[n, k] a[k-1], {k, n}]];
Table[a@n, {n, 0, 30}] (* Robert G. Wilson v, May 27 2009 *)

Prog

(SageMath)
@CachedFunction # a = A159666
def a(n): return 1 if (n==0) else sum(binomial(n, j)*gcd(n, j)*a(j-1) for j in range(1, n+1))
[a(n) for n in range(40)] # G. C. Greubel, Sep 26 2022

Crossrefs

Cf. A159667.

Sequence in context: A229286 A191365 A335459 * A349021 A316186 A231274

Adjacent sequences: A159663 A159664 A159665 * A159667 A159668 A159669

Keyword

nonn

Author

Leroy Quet, Apr 19 2009

Extensions

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

Status

approved