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A283263 Expansion of exp( Sum_{n>=1} -sigma_3(n)*x^n/n ) in powers of x. 11
1, -1, -4, -5, -1, 21, 49, 81, 45, -121, -484, -997, -1344, -840, 1624, 6931, 15149, 23155, 23469, 2240, -57596, -168929, -322587, -461165, -450668, -64135, 985621, 2935044, 5718865, 8597971, 9683008, 5596899, -8414092, -37295629, -83336988, -141108721 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: Product_{n>=1} (1 - x^n)^(n^2).

a(n) = -(1/n)*Sum_{k=1..n} sigma_3(k)*a(n-k).

MATHEMATICA

a[n_] := If[n<1, 1, -(1/n) * Sum[DivisorSigma[3, k] a[n - k], {k, n}]]; Table[a[n], {n, 0, 35}] (* Indranil Ghosh, Mar 16 2017 *)

PROG

(PARI) a(n) = if(n<1, 1, -(1/n) * sum(k=1, n, sigma(k, 3) * a(n - k)));

for(n=0, 35, print1(a(n), ", ")) \\ Indranil Ghosh, Mar 16 2017

(SageMath) # uses[EulerTransform from A166861]

b = EulerTransform(lambda n: -n^2)

print([b(n) for n in range(36)]) # Peter Luschny, Nov 11 2020

CROSSREFS

Column k=2 of A283272.

Cf. A023871 (exp( Sum_{n>=1} sigma_3(n)*x^n/n )).

Cf. exp( Sum_{n>=1} -sigma_k(n)*x^n/n ): A010815 (k=1), A073592 (k=2), this sequence (k=3), A283264 (k=4), A283271 (k=5).

Sequence in context: A234937 A210590 A108446 * A109962 A102230 A147724

Adjacent sequences:  A283260 A283261 A283262 * A283264 A283265 A283266

KEYWORD

sign

AUTHOR

Seiichi Manyama, Mar 04 2017

STATUS

approved

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Last modified May 7 08:57 EDT 2021. Contains 343636 sequences. (Running on oeis4.)