OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..200
FORMULA
a(n) ~ 3^(4*n - 1/2) / (sqrt(Pi) * n^(5/2) * 2^(2*n + 2)). - Vaclav Kotesovec, Jun 01 2022
MATHEMATICA
seq[n_] := Module[{p, q}, p = 1 + InverseSeries[x/(3*(1 + x)^3) + O[x]^n]; q = x*D[p, x]/p; Integrate[((p - 1)/3 + Sum[EulerPhi[d]*(q /. x -> x^d + O[x]^n), {d, 2, n}])/x, x] + 1];
CoefficientList[seq[21], x] (* Jean-François Alcover, Jul 05 2018, after Andrew Howroyd *)
PROG
(PARI)
seq(n)={ my(p=1 + serreverse( x/(3*(1 + x)^3) + O(x*x^n) )); my(q=x*deriv(p)/p);
Vec(intformal(((p-1)/3 + sum(d=2, n, eulerphi(d)*subst(q, x, x^d+O(x*x^n))))/x) + 1)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, May 01 2018
STATUS
approved