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A047654 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^2 in powers of x. 4
1, -2, 1, 0, -2, 2, -2, 2, 1, 0, 2, -2, 3, 0, 2, 0, 0, 2, -2, 0, -2, 2, -1, 0, 0, -2, -2, -2, 1, -2, 0, -2, -2, 0, 2, 0, -2, 0, -2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, -2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, -4, 0, 0, 2, 1, -2, 0, -2, 0, 0, 0, 0, 2, -4, 1, 0, 0, -2, -2, -2, -2, 0, 0, -2, 0, 2, -2, 2, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..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, 2):

seq(a(n), n=2..94);  # Alois P. Heinz, Feb 07 2021

MATHEMATICA

nmax = 94; CoefficientList[Series[(Product[(1 - (-x)^j), {j, 1, nmax}] - 1)^2, {x, 0, nmax}], x] // Drop[#, 2] & (* Ilya Gutkovskiy, Feb 07 2021 *)

PROG

(PARI) seq(n)={Vec((prod(j=1, n, 1-(-x)^j + O(x^n)) - 1)^2)} \\ Andrew Howroyd, Feb 07 2021

CROSSREFS

Cf. A047655, A001482, A001483, A001484, A001485, A001486, A001487, A001488.

Sequence in context: A275409 A029343 A137992 * A058487 A062243 A128095

Adjacent sequences:  A047651 A047652 A047653 * A047655 A047656 A047657

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 June 19 21:32 EDT 2021. Contains 345151 sequences. (Running on oeis4.)