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A047639 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^14 in powers of x. 1
1, -14, 91, -364, 987, -1820, 1897, 754, -8008, 18928, -26845, 19460, 15015, -76272, 141065, -163072, 90727, 99386, -368277, 602616, -643734, 358190, 274547, -1101100, 1801086, -1982330, 1344525, 148316, -2163590, 4032756, -4938843, 4216576 (list; graph; refs; listen; history; text; internal format)
OFFSET

14,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 14..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, 14):

seq(a(n), n=14..45);  # Alois P. Heinz, Feb 07 2021

MATHEMATICA

nmax = 45; CoefficientList[Series[(Product[(1 - (-x)^j), {j, 1, nmax}] - 1)^14, {x, 0, nmax}], x] // Drop[#, 14] & (* Ilya Gutkovskiy, Feb 07 2021 *)

CROSSREFS

Sequence in context: A200191 A266805 A301380 * A202291 A010930 A220892

Adjacent sequences:  A047636 A047637 A047638 * A047640 A047641 A047642

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 December 4 19:40 EST 2021. Contains 349526 sequences. (Running on oeis4.)