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A293604 E.g.f.: exp(x * (1 - x)). 2

%I

%S 1,1,-1,-5,1,41,31,-461,-895,6481,22591,-107029,-604031,1964665,

%T 17669471,-37341149,-567425279,627491489,19919950975,-2669742629,

%U -759627879679,-652838174519,31251532771999,59976412450835,-1377594095061119,-4256461892701199

%N E.g.f.: exp(x * (1 - x)).

%H Seiichi Manyama, <a href="/A293604/b293604.txt">Table of n, a(n) for n = 0..732</a>

%F a(n) = (-1)^n * A000321(n).

%F a(n) = a(n-1) - 2 * (n-1) * a(n-2) for n > 1.

%F E.g.f.: Product_{k>=1} (1 + x^k)^(mu(k)/k). - _Ilya Gutkovskiy_, May 23 2019

%t CoefficientList[Series[E^(x*(1-x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Oct 13 2017 *)

%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x*(1-x))))

%o (PARI) a(n) = (-1)^n*polhermite(n, -1/2); \\ _Michel Marcus_, Oct 13 2017

%Y Cf. A111884, A293571, A293572, A293573.

%Y Cf. A000321.

%K sign

%O 0,4

%A _Seiichi Manyama_, Oct 12 2017

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Last modified June 18 10:54 EDT 2021. Contains 345098 sequences. (Running on oeis4.)