A340994 a(n) is the (2n)-th term of the n-fold self-convolution of the Euler totient function phi.

1, 1, 5, 19, 89, 391, 1817, 8429, 39697, 187849, 894965, 4282191, 20572961, 99158645, 479294877, 2322365959, 11276837761, 54860498415, 267336028565, 1304677123305, 6375749480369, 31195075605755, 152798541606529, 749184538847397, 3676699991008897

Offset: 0

Author

Alois P. Heinz, Feb 01 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1431

Crossrefs

Cf. A000010, A008683, A340995.

Programs

Maple

b:= proc(n, k) option remember; `if`(k=0, 1,
      `if`(k=1, numtheory[phi](n+1), (q->
       add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..29);

Formula

a(n) = [x^(2n)] (Sum_{j>=1} mu(j)*x^j/(1-x^j)^2)^n.

a(n) = A340995(2n,n).

a(n) ~ c * d^n / sqrt(n), where d = 5.0117569538757703168577972551675369123003378927616324330274512382246419... and c = 0.287455327702489527773675891801880332800309441856159133456758815116... - Vaclav Kotesovec, Aug 18 2021