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 A047649 Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^11 in powers of x. 23
 1, -11, 55, -165, 319, -352, -44, 1100, -2585, 3542, -2519, -1530, 8085, -14410, 16170, -9460, -6644, 28105, -46145, 50248, -32802, -6193, 57200, -102575, 121968, -100397, 35123, 60390, -158840, 226413, -234344, 168773, -37070, -131175, 290851, -391402 (list; graph; refs; listen; history; text; internal format)
 OFFSET 11,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 11..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. FORMULA a(n) = [x^n]( QPochhammer(-x) - 1 )^11. - G. C. Greubel, Sep 05 2023 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, 11): seq(a(n), n=11..46); # Alois P. Heinz, Feb 07 2021 MATHEMATICA nmax=46; CoefficientList[Series[(Product[(1-(-x)^j), {j, nmax}] - 1)^11, {x, 0, nmax}], x]//Drop[#, 11] & (* Ilya Gutkovskiy, Feb 07 2021 *) With[{k=11}, Drop[CoefficientList[Series[(QPochhammer[-x] -1)^k, {x, 0, 75}], x], k]] (* G. C. Greubel, Sep 05 2023 *) PROG (Magma) m:=75; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^(11) )); // G. C. Greubel, Sep 05 2023 (SageMath) from sage.modular.etaproducts import qexp_eta m=75; k=11; def f(k, x): return (-1 + qexp_eta(QQ[['q']], m+2).subs(q=-x) )^k def A047649_list(prec): P. = PowerSeriesRing(QQ, prec) return P( f(k, x) ).list() a=A047649_list(m); a[k:] # G. C. Greubel, Sep 05 2023 (PARI) my(N=55, x='x+O('x^N)); Vec((eta(-x)-1)^11) \\ Joerg Arndt, Sep 05 2023 CROSSREFS Cf. A001482 - A001488, A001490, A047638 - A047648, A047654, A047655, A341243. Sequence in context: A246406 A255415 A153449 * A010927 A009550 A226255 Adjacent sequences: A047646 A047647 A047648 * A047650 A047651 A047652 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 September 17 21:09 EDT 2024. Contains 375990 sequences. (Running on oeis4.)