A301594 - OEIS

A301594

Expansion of Product_{k>=1} (1 + x^k)^A001615(k), where A001615 is the Dedekind psi function.

1, 1, 3, 7, 13, 27, 55, 99, 185, 341, 604, 1064, 1863, 3181, 5411, 9123, 15167, 25051, 41083, 66715, 107703, 172735, 275034, 435484, 685753, 1073481, 1672160, 2592070, 3998278, 6140196, 9389302, 14296376, 21682534, 32759202, 49308812, 73956692, 110545113

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OFFSET

0,3

LINKS

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

FORMULA

a(n) ~ exp(3^(5/3) * (5*Zeta(3))^(1/3) * n^(2/3) / (2^(4/3) * Pi^(2/3)) - Pi^(2/3) * n^(1/3) / (2^(5/3) * 3^(2/3) * (5*Zeta(3))^(1/3)) - Pi^2 / (2160 * Zeta(3))) * (5*Zeta(3))^(1/6) / (2^(3/4) * 3^(1/6) * Pi^(5/6) * n^(2/3)).

MATHEMATICA

nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[k*Sum[MoebiusMu[d]^2 / d, {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. A001615, A156303.

Sequence in context: A298360 A140465 A333653 * A080241 A098479 A119445

Adjacent sequences: A301591 A301592 A301593 * A301595 A301596 A301597

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 24 2018

STATUS

approved