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

0,3

Links

Table of n, a(n) for n=0..19.

Formula

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

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 *)

Prog

(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;

Crossrefs

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

Sequence in context: A286764 A180609 A074540 * A218680 A141003 A002404

Adjacent sequences: A353189 A353190 A353191 * A353193 A353194 A353195

Keyword

nonn

Author

Seiichi Manyama, Apr 29 2022

Status

approved