A301978 Euler transform of A065958.

1, 1, 6, 16, 51, 127, 367, 897, 2342, 5662, 13894, 32656, 77076, 176586, 403526, 904140, 2013267, 4418167, 9628682, 20741434, 44362988, 93984842, 197731390, 412619250, 855408327, 1760687593, 3601827236, 7321181534, 14796204874, 29730215150, 59419375058

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

G.f.: Product_{k>=1} 1/(1-x^k)^A065958(k).

a(n) ~ exp(4*(7*Zeta(3))^(1/4) * n^(3/4) / sqrt(3*Pi) - sqrt(Pi) * n^(1/4) / (4*3^(3/2) * (7*Zeta(3))^(1/4)) - Zeta(3) / (4*Pi^2)) * 3^(1/4) * (7*Zeta(3))^(1/8) / (2^(3/2) * Pi^(3/4) * n^(5/8)).

Mathematica

nmax = 40; CoefficientList[Series[Exp[Sum[Sum[Sum[MoebiusMu[k/d]^2*d^2, {d, Divisors@k}] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 31 2018 *)

Crossrefs

Cf. A065958, A156733, A301980.

Sequence in context: A341657 A288572 A367993 * A275585 A026086 A175659

Adjacent sequences: A301975 A301976 A301977 * A301979 A301980 A301981

Keyword

nonn

Author

Vaclav Kotesovec, Mar 30 2018

Status

approved