A338814 Expansion of e.g.f. log(Product_{k>0} (1 + x^k)^(1/k)).

1, 0, 4, -6, 48, 0, 1440, -10080, 120960, 0, 7257600, -79833600, 958003200, 0, 348713164800, -3923023104000, 41845579776000, 0, 12804747411456000, -243290200817664000, 9731608032706560000, 0, 2248001455555215360000, -103408066955539906560000

Offset: 1

Author

Seiichi Manyama, Nov 10 2020

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..450

Crossrefs

Column 1 of A338813.

Cf. A048272, A168243, A318249.

Programs

Mathematica

a[n_] := (n - 1)! * DivisorSum[n, (-1)^(# + 1) &]; Array[a, 25] (* Amiram Eldar, Apr 28 2021 *)

PARI

N=40; x='x+O('x^N); Vec(serlaplace(log(prod(k=1, N, (1+x^k)^(1/k)))))

PARI

{a(n) = if(n<1, 0, (n-1)!*sumdiv(n, d, (-1)^(d+1)))}

Formula

a(n) = (n-1)! * A048272(n).