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A022662 Expansion of Product_{m>=1} (1 - m*q^m)^2. 3
1, -2, -3, 2, 4, 16, -3, 6, -31, -72, -15, -44, 9, 154, 521, 48, 426, 66, 2, -1618, -3782, -210, -3882, -1282, 1119, 3940, 10867, 37208, 11647, 20574, 6256, 534, -1915, -120006, -161755, -312622, -93923, -271850, -25782, -197026, 1112303, 574604, 209604, 3038822, 4187500, 1398330 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: exp(-2*Sum_{j>=1} Sum_{k>=1} k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 07 2018

MATHEMATICA

nmax = 50; poly = ConstantArray[0, nmax+1]; poly[[1]] = 1; poly[[2]] = -2; poly[[3]] = 1; Do[Do[Do[poly[[j+1]] -= k*poly[[j-k+1]], {j, nmax, k, -1}]; , {p, 1, 2}], {k, 2, nmax}]; poly  (* Vaclav Kotesovec, Jan 07 2016 *)

With[{nmax = 50}, CoefficientList[Series[Product[(1 - k*q^k)^2, {k, 1, nmax}], {q, 0, nmax}], q]] (* G. C. Greubel, Feb 18 2018 *)

PROG

(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1-n*q^n)^2)) \\ G. C. Greubel, Feb 18 2018

(MAGMA) Coefficients(&*[(1-m*x^m)^2:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 18 2018

CROSSREFS

Cf. A022662, A022726.

Column k=2 of A297323.

Sequence in context: A236406 A247497 A202714 * A295703 A059051 A130069

Adjacent sequences:  A022659 A022660 A022661 * A022663 A022664 A022665

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 22 04:04 EDT 2019. Contains 322329 sequences. (Running on oeis4.)