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A001482 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^4 in powers of x.
(Formerly M3263 N1317)
26
1, -4, 6, -4, -3, 12, -16, 16, -6, -8, 18, -28, 26, -20, 2, 12, -23, 32, -36, 28, -6, 4, 22, -20, 39, -32, 32, -12, 2, 16, -12, 24, -40, 28, -34, 0, -6, -16, 0, -40, 6, -36, 26, -32, -5, 0, -20, 8, -16, 12, -10, 40, -22, 12, 14, 12, 45, 16, 38, 4, 12, 0, 34, 8, 38, 12, -24, 44, 2, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

REFERENCES

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..10000

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

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, 4):

seq(a(n), n=4..73);  # Alois P. Heinz, Feb 07 2021

MATHEMATICA

nmax = 73; CoefficientList[Series[(Product[(1 - (-x)^j), {j, 1, nmax}] - 1)^4, {x, 0, nmax}], x] // Drop[#, 4] & (* Ilya Gutkovskiy, Feb 07 2021 *)

CROSSREFS

Sequence in context: A199721 A187147 A128633 * A198493 A161965 A256419

Adjacent sequences:  A001479 A001480 A001481 * A001483 A001484 A001485

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 15 02:21 EDT 2021. Contains 343909 sequences. (Running on oeis4.)