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A293571 E.g.f.: exp(x/(1 + x + x^2)). 4

%I

%S 1,1,-1,-5,25,41,-1049,2899,54545,-610415,-1363409,92652011,

%T -651996311,-10663181255,262674487895,-529402905149,-68312606260319,

%U 1136414207246369,7701376416944095,-584076369474366245,6461047290787787321,173442620419212050761

%N E.g.f.: exp(x/(1 + x + x^2)).

%H Robert Israel, <a href="/A293571/b293571.txt">Table of n, a(n) for n = 0..446</a>

%H Robert Israel, <a href="/A293571/a293571.png">Plot of a(n)/(n! exp(sqrt(n))) for n = 2 .. 2500</a>

%F E.g.f.: Product_{k>0} exp(x^(3*k-2)) / exp(x^(3*k-1)).

%F a(n) = (3-2*n)*a(n-1) - 3*(n-2)*(n-1)*a(n-2) + (5-2*n)*(n-1)*(n-2)*a(n-3) - (n-4)*(n-3)*(n-2)*(n-1)*a(n-4). - _Robert Israel_, Jul 27 2020

%p f:= gfun:-rectoproc({a(n) = (3-2*n)*a(n-1) - 3*(n-2)*(n-1)*a(n-2) + (5-2*n)*(n-1)*(n-2)*a(n-3)- (n-4)*(n-3)*(n-2)*(n-1)*a(n-4),a(0)=1,a(1)=1,a(2)=-1,a(3)=-5},a(n),remember):

%p map(f, [$0..30]); # _Robert Israel_, Jul 27 2020

%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(x/(1+x+x^2))))

%o (PARI) N=66; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, exp(x^(3*k-2)-x^(3*k-1)))))

%Y Cf. A111884, A293572, A293573.

%K sign

%O 0,4

%A _Seiichi Manyama_, Oct 12 2017

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Last modified August 2 15:26 EDT 2021. Contains 346428 sequences. (Running on oeis4.)