A352887 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, 14, 84, 634, 5740, 60626, 731852, 9938670, 149966116, 2489148386, 45070961740, 884107377360, 18676602726734, 422721143355808, 10205605681874952, 261789688633794528, 7110331886095458918, 203848868169846041430, 6151813078359073154568

Offset: 0

Author

Seiichi Manyama, Apr 07 2022

Keywords

• nonn

Crossrefs

Cf. A000010, A159929, A300011, A318811.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, eulerphi(k)*x^k/k!))))

PARI

a(n) = if(n==0, 1, sum(k=1, n, eulerphi(k)*binomial(n, k)*a(n-k)));

Formula

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