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A047655 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^3 in powers of x. 5
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, -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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..10000

H. Gupta, On the coefficients of the powers of Dedekind's modular form (annotated and scanned copy)

H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.

MAPLE

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

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

    end:

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

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

    end:

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

seq(a(n), n=3..92);  # Alois P. Heinz, Feb 07 2021

MATHEMATICA

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

CROSSREFS

Sequence in context: A245668 A002102 A332552 * A078685 A078882 A262220

Adjacent sequences:  A047652 A047653 A047654 * A047656 A047657 A047658

KEYWORD

sign

AUTHOR

N. J. A. Sloane

EXTENSIONS

Definition and offset edited by Ilya Gutkovskiy, Feb 07 2021

STATUS

approved

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)