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

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

Prog

(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)));

Crossrefs

Cf. A000010, A159929, A300011, A318811.

Sequence in context: A111538 A354003 A324237 * A230218 A301934 A160881

Adjacent sequences: A352884 A352885 A352886 * A352888 A352889 A352890

Keyword

nonn

Author

Seiichi Manyama, Apr 07 2022

Status

approved