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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..424

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...

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]!

Crossrefs

Cf. A318917, A377507, A377509.

Cf. A178933, A358714.

Sequence in context: A196585 A197042 A350549 * A062189 A203605 A373614

Adjacent sequences: A377505 A377506 A377507 * A377509 A377510 A377511

Keyword

nonn

Author

Vaclav Kotesovec, Oct 30 2024

Status

approved