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A185654 G.f.: exp( Sum_{n>=1} -sigma(3n)*x^n/n ). 9
1, -4, 2, 9, -9, -2, 0, -5, 9, 9, 0, -9, -1, -9, 0, -1, 9, 9, -9, 9, 0, 9, -5, -18, -18, 9, 7, 0, 9, 0, 0, 9, 9, -18, 18, -7, -9, -9, -9, 9, -4, -9, -9, 18, 9, 0, 18, 9, 0, -9, -9, -8, -9, 18, -9, 9, -18, 1, -9, -18, 9, 0, 18, 18, 0, 0, 9, -9, 18, -9, 5, -9, 0, -9, -9, -9, -18, 11, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: E(x)^4/E(x^3) where E(x) = Product_{n>=1} (1-x^n). [From a formula by Joerg Arndt in A182819]
a(n) = -(1/n)*Sum_{k=1..n} sigma(3*k)*a(n-k). - Seiichi Manyama, Mar 04 2017
Expansion of E(x) * E(x*w) * E(x/w) in powers of x^3 where w = exp(2 Pi i / 3). - Michael Somos, Jul 12 2018
EXAMPLE
G.f. = 1 - 4*x + 2*x^2 + 9*x^3 - 9*x^4 - 2*x^5 - 5*x^7 + 9*x^8 + ... - Michael Somos, Jul 12 2018
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ x]^4 / QPochhammer[ x^3], {x, 0, n}]; (* Michael Somos, Jul 12 2018 *)
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n, -sigma(3*m)*x^m/m)+x*O(x^n)), n)}
(PARI) {a(n)=local(X=x+x*O(x^n)); polcoeff(eta(X)^4/eta(X^3), n)}
CROSSREFS
Cf. Product_{n>=1} (1 - q^n)^(k+1)/(1 - q^(k*n)): A010815 (k=1), A115110 (k=2), this sequence (k=3), A282937 (k=5), A282942 (k=7).
Sequence in context: A290538 A097664 A144811 * A228041 A242049 A179398
KEYWORD
sign
AUTHOR
Paul D. Hanna, Feb 16 2011
STATUS
approved

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Last modified April 17 11:15 EDT 2024. Contains 371763 sequences. (Running on oeis4.)