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

%I A340994 #13 Aug 18 2021 12:27:04
%S A340994 1,1,5,19,89,391,1817,8429,39697,187849,894965,4282191,20572961,
%T A340994 99158645,479294877,2322365959,11276837761,54860498415,267336028565,
%U A340994 1304677123305,6375749480369,31195075605755,152798541606529,749184538847397,3676699991008897
%N A340994 a(n) is the (2n)-th term of the n-fold self-convolution of the Euler totient function phi.
%H A340994 Alois P. Heinz, <a href="/A340994/b340994.txt">Table of n, a(n) for n = 0..1431</a>
%F A340994 a(n) = [x^(2n)] (Sum_{j>=1} mu(j)*x^j/(1-x^j)^2)^n.
%F A340994 a(n) = A340995(2n,n).
%F A340994 a(n) ~ c * d^n / sqrt(n), where d = 5.0117569538757703168577972551675369123003378927616324330274512382246419... and c = 0.287455327702489527773675891801880332800309441856159133456758815116... - _Vaclav Kotesovec_, Aug 18 2021
%p A340994 b:= proc(n, k) option remember; `if`(k=0, 1,
%p A340994       `if`(k=1, numtheory[phi](n+1), (q->
%p A340994        add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
%p A340994     end:
%p A340994 a:= n-> b(n$2):
%p A340994 seq(a(n), n=0..29);
%Y A340994 Cf. A000010, A008683, A340995.
%K A340994 nonn
%O A340994 0,3
%A A340994 _Alois P. Heinz_, Feb 01 2021