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A047655 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^3 in powers of x. 5

%I

%S 1,-3,3,-1,-3,6,-6,6,0,-3,6,-9,8,-6,0,0,-6,6,-13,3,-6,3,0,-3,6,-9,6,

%T -3,6,0,6,6,-3,11,0,6,0,9,0,0,0,-3,13,0,0,-6,0,-6,3,-3,-6,0,-15,-6,-3,

%U 0,-6,0,-6,0,-6,-6,0,-11,0,0,-6,0,6,0,6,0,0,0,-3,19,12,-3,0,0,6,6,6,6,0,0,6,0,21,3

%N Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^3 in powers of x.

%H Alois P. Heinz, <a href="/A047655/b047655.txt">Table of n, a(n) for n = 3..10000</a>

%H H. Gupta, <a href="/A001482/a001482.pdf">On the coefficients of the powers of Dedekind's modular form</a> (annotated and scanned copy)

%H H. Gupta, <a href="http://jlms.oxfordjournals.org/content/s1-39/1/433.extract">On the coefficients of the powers of Dedekind's modular form</a>, J. London Math. Soc., 39 (1964), 433-440.

%p g:= proc(n) option remember; `if`(n=0, 1, add(add([-d, d, -2*d, d]

%p [1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)

%p end:

%p b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0, g(n)),

%p (q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))

%p end:

%p a:= n-> b(n, 3):

%p seq(a(n), n=3..92); # _Alois P. Heinz_, Feb 07 2021

%t nmax = 92; CoefficientList[Series[(Product[(1 - (-x)^j), {j, 1, nmax}] - 1)^3, {x, 0, nmax}], x] // Drop[#, 3] & (* _Ilya Gutkovskiy_, Feb 07 2021 *)

%K sign

%O 3,2

%A _N. J. A. Sloane_

%E Definition and offset edited by _Ilya Gutkovskiy_, Feb 07 2021

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Last modified June 24 06:16 EDT 2021. Contains 345416 sequences. (Running on oeis4.)