login
A131681
a(n) = phi(binomial(2*n,n)*n^2).
1
0, 1, 8, 48, 384, 1440, 8640, 40320, 184320, 829440, 5529600, 18247680, 87588864, 474439680, 1532805120, 7664025600, 32699842560, 130288435200, 517321728000, 2184247296000, 9196830720000, 38626689024000, 188841590784000, 888413847552000, 3876714971136000
OFFSET
0,3
LINKS
FORMULA
a(n) = A000010(A002736(n)).
MAPLE
with(numtheory):with(combinat):a:=n->phi(binomial(2*n, n)*n^2): seq(a(n), n=0..25);
MATHEMATICA
Table[EulerPhi[n^2*Binomial[2*n, n]], {n, 0, 40}] (* G. C. Greubel, Nov 29 2025 *)
PROG
(Magma)
A131681:= func< n | n eq 0 select 0 else EulerPhi(n^2*(n+1)*Catalan(n)) >;
[A131681(n): n in [0..40]]; // G. C. Greubel, Nov 29 2025
(SageMath)
def A131681(n): return euler_phi(n^2*binomial(2*n, n))
print([A131681(n) for n in range(41)]) # G. C. Greubel, Nov 29 2025
CROSSREFS
Sequence in context: A200161 A172111 A144014 * A382134 A077708 A165041
KEYWORD
nonn
AUTHOR
Zerinvary Lajos, Oct 07 2007
STATUS
approved