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%I #12 Aug 20 2021 06:59:43
%S 1,1,4,10,44,156,752,3256,17040,84496,475712,2611104,15687872,
%T 93376960,594638592,3786534784,25412227328,171474649344,1206965027840,
%U 8569374206464,63003419470848,468111364627456,3582366347030528,27733474149611520,220255800262627328
%N Expansion of e.g.f.: exp(x^2)*(exp(2*x)+1)/2.
%H C.-O. Chow, <a href="https://doi.org/10.1016/j.disc.2006.04.018">Counting involutory, unimodal and alternating signed permutations</a>, Discr. Math. 306 (2006), 2222-2228.
%F a(n) ~ exp(sqrt(2*n)-n/2-1/2)*2^(n/2-3/2)*n^(n/2). - _Vaclav Kotesovec_, Jun 27 2013
%F Conjecture: D-finite with recurrence a(n) -2*a(n-1) +2*(-2*n+3)*a(n-2) +4*(n-2)*a(n-3) +4*(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Aug 20 2021
%t CoefficientList[Series[E^(x^2)*(E^(2*x)+1)/2, {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 27 2013 *)
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(x^2)*(exp(2*x)+1)/2))) \\ _Michel Marcus_, May 28 2019
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Sep 22 2006
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