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

0,3

Links

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

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

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);

Crossrefs

Cf. A000010, A008683, A340995.

Sequence in context: A149803 A259204 A149804 * A301702 A296162 A144036

Adjacent sequences: A340991 A340992 A340993 * A340995 A340996 A340997

Keyword

nonn

Author

Alois P. Heinz, Feb 01 2021

Status

approved