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%I #31 Sep 08 2022 08:46:19
%S 1,-1,-4,-23,-229,-2761,-42615,-758499,-15702086,-365588036,
%T -9516954786,-273061566624,-8575969258607,-292418459301779,
%U -10762887030763337,-425243370397722674,-17953905924215881215,-806666656048846472309
%N Expansion of Product_{k>=1} (1 - k^k*x^k).
%H Seiichi Manyama, <a href="/A292312/b292312.txt">Table of n, a(n) for n = 0..386</a>
%F Convolution inverse of A023882.
%F a(n) ~ -n^n * (1 - exp(-1)/n - (exp(-1)/2 + 4*exp(-2))/n^2). - _Vaclav Kotesovec_, Sep 14 2017
%F a(0) = 1 and a(n) = -(1/n) * Sum_{k=1..n} A294645(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Nov 09 2017
%p seq(coeff(series(mul((1-k^k*x^k),k=1..n),x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Oct 31 2018
%t terms = 18; CoefficientList[Product[(1 - k^k*x^k), {k, 1, terms}] + O[x]^(terms), x] (* _Jean-François Alcover_, Nov 11 2017 *)
%o (PARI) {a(n) = polcoeff(prod(k=1, n, 1-k^k*x^k+x*O(x^n)), n)}
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R! ( (&*[(1 - k^k*x^k): k in [1..m]]) )); // _G. C. Greubel_, Oct 31 2018
%Y Column k=1 of A294653.
%Y Cf. A023882, A265949.
%K sign
%O 0,3
%A _Seiichi Manyama_, Sep 14 2017
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