A377507 Expansion of e.g.f. exp(Sum_{k>=1} phi(k)^2 * x^k/k), where phi is the Euler totient function A000010.
1, 1, 2, 12, 66, 690, 4860, 63000, 711900, 8876700, 131405400, 2160219600, 37553808600, 686750664600, 13805424032400, 278759396916000, 6445702905642000, 150985820419434000, 3825993309462324000, 99427990563910008000, 2724045313186016820000, 78032929885709378580000
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..435
Programs
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Mathematica
nmax = 25; $RecursionLimit->Infinity; a[n_]:=a[n]=If[n==0, 1, Sum[EulerPhi[k]^2*a[n-k], {k, 1, n}]/n];Table[a[n]*n!, {n, 0, nmax}] nmax = 25; CoefficientList[Series[Exp[Sum[EulerPhi[k]^2 * x^k / k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!
Formula
log(a(n)/n!) ~ 3 * c^(1/3) * n^(2/3) / 2^(2/3), where c = Product_{p primes} (1 - 2/p^2 + 1/p^3) = A065464 = 0.428249505677094440218765707581823546121298...