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A047641 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^16 in powers of x. 1
1, -16, 120, -560, 1804, -4128, 6312, -3920, -10530, 42208, -82752, 99584, -39460, -141200, 422568, -673936, 660941, -144720, -938840, 2301568, -3257188, 2916592, -628040, -3492160, 8217536, -11341568, 10408280, -3885040, -7668720, 21033408 (list; graph; refs; listen; history; text; internal format)
OFFSET

16,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 16..10000

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

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, 16):

seq(a(n), n=16..45);  # Alois P. Heinz, Feb 07 2021

MATHEMATICA

nmax = 45; CoefficientList[Series[(Product[(1 - (-x)^j), {j, 1, nmax}] - 1)^16, {x, 0, nmax}], x] // Drop[#, 16] & (* Ilya Gutkovskiy, Feb 07 2021 *)

CROSSREFS

Sequence in context: A190049 A317227 A138571 * A010932 A014805 A022611

Adjacent sequences:  A047638 A047639 A047640 * A047642 A047643 A047644

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 July 4 12:21 EDT 2022. Contains 355075 sequences. (Running on oeis4.)