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A301594 Expansion of Product_{k>=1} (1 + x^k)^A001615(k), where A001615 is the Dedekind psi function. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A068673 A298360 A140465 * A080241 A098479 A119445

Adjacent sequences:  A301591 A301592 A301593 * A301595 A301596 A301597

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 24 2018

STATUS

approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)