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A338814 Expansion of e.g.f. log(Product_{k>0} (1 + x^k)^(1/k)). 3
1, 0, 4, -6, 48, 0, 1440, -10080, 120960, 0, 7257600, -79833600, 958003200, 0, 348713164800, -3923023104000, 41845579776000, 0, 12804747411456000, -243290200817664000, 9731608032706560000, 0, 2248001455555215360000, -103408066955539906560000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

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

MATHEMATICA

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

PROG

(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)))}

CROSSREFS

Column 1 of A338813.

Cf. A048272, A168243, A318249.

Sequence in context: A174653 A274215 A119944 * A134592 A306705 A165658

Adjacent sequences:  A338811 A338812 A338813 * A338815 A338816 A338817

KEYWORD

sign

AUTHOR

Seiichi Manyama, Nov 10 2020

STATUS

approved

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Last modified May 18 22:37 EDT 2022. Contains 353826 sequences. (Running on oeis4.)