A353192 Expansion of e.g.f. 1/(1 - Sum_{k>=1} phi(k) * x^k / k), where phi is the Euler totient function A000010.

1, 1, 3, 16, 110, 986, 10202, 126288, 1770120, 27939192, 489658632, 9455296896, 198951693360, 4537680805776, 111426422418768, 2931467216681856, 82273083792879744, 2453340521239749504, 77458777017799833216, 2581489882182061744128

Offset: 0

Author

Seiichi Manyama, Apr 29 2022

Keywords

• nonn

Crossrefs

Cf. A000010, A074930, A159929, A318917, A352887.

Programs

Mathematica

phi[k_] := phi[k] = EulerPhi[k]; a[0] = 1; a[n_] := a[n] = Sum[(k - 1)! * phi[k] * Binomial[n, k] * a[n - k], {k, 1, n}]; Array[a, 20, 0] (* Amiram Eldar, Apr 30 2022 *)

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, eulerphi(k)*x^k/k))))

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (j-1)!*eulerphi(j)*binomial(i, j)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A074930(k) * binomial(n,k) * a(n-k).