A377509 Expansion of e.g.f. exp(Sum_{k>=1} phi(k)^4 * x^k/k), where phi is the Euler totient function A000010.

1, 1, 2, 36, 234, 7290, 54540, 1408680, 23119740, 341788860, 11790437400, 231972879600, 8206299070200, 191673262380600, 6154270418696400, 206515993375692000, 6574758436640394000, 269828090984990538000, 9531096165082736244000, 411037724983993923816000

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..412

Formula

log(a(n)/n!) ~ 5 * 3^(1/5) * c^(1/5) * n^(4/5) / 2^(7/5), where c = Product_{primes p} (1 - 4/p^2 + 6/p^3 - 4/p^4 + 1/p^5) = 0.286256471511560891173288340086638647956...

Mathematica

nmax = 25; $RecursionLimit->Infinity; a[n_]:=a[n]=If[n==0, 1, Sum[EulerPhi[k]^4 * a[n-k], {k, 1, n}]/n]; Table[a[n]*n!, {n, 0, nmax}]
nmax = 25; CoefficientList[Series[Exp[Sum[EulerPhi[k]^4 * x^k / k, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!

Crossrefs

Cf. A318917, A377507, A377508.

Cf. A205797, A361148.

Sequence in context: A025531 A099903 A341535 * A074426 A082636 A242533

Adjacent sequences: A377506 A377507 A377508 * A377510 A377511 A377512

Keyword

nonn

Author

Vaclav Kotesovec, Oct 30 2024

Status

approved