A377508 Expansion of e.g.f. exp(Sum_{k>=1} phi(k)^3 * x^k/k), where phi is the Euler totient function A000010.
1, 1, 2, 20, 122, 2122, 15532, 284104, 3837500, 52963964, 1125315224, 20981180464, 500475045688, 10373180665720, 264908485440848, 6624880728277088, 185812008437953808, 5449866267968244496, 167510440639938875680, 5447433174773217714496, 177500241844579492474016
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..424
Programs
-
Mathematica
nmax = 25; $RecursionLimit->Infinity; a[n_]:=a[n]=If[n==0, 1, Sum[EulerPhi[k]^3*a[n-k], {k, 1, n}]/n];Table[a[n]*n!, {n, 0, nmax}] nmax = 25; CoefficientList[Series[Exp[Sum[EulerPhi[k]^3 * x^k / k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!
Formula
log(a(n)/n!) ~ 2^(9/4) * c^(1/4) * n^(3/4) / 3^(3/4), where c = Product_{p primes} (1 - 3/p^2 + 3/p^3 - 1/p^4) = 0.337187873791589971961692816152158244949154127758...