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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..435

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...

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]!

Crossrefs

Cf. A318917, A377508, A377509.

Cf. A065464, A127473, A156302.

Sequence in context: A039633 A265451 A180195 * A212389 A241074 A020062

Adjacent sequences: A377504 A377505 A377506 * A377508 A377509 A377510

Keyword

nonn

Author

Vaclav Kotesovec, Oct 30 2024

Status

approved