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%I #11 Sep 17 2022 08:48:26
%S 1,0,2,6,3096,61560,65248200,4058986680,7506140268480,
%T 1062517243193280,3052268000677879200,822543740977513816800,
%U 3395913346775619237617280,1553795963458841732838848640,8727392877498334693600263757440
%N a(n) = n! * Sum_{k=0..floor(n/2)} k^(2*n)/k!.
%F E.g.f.: Sum_{k>=0} (k^2 * x)^(2 * k) / (k! * (1 - k^2 * x)).
%o (PARI) a(n) = n!*sum(k=0, n\2, k^(2*n)/k!);
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k^2*x)^(2*k)/(k!*(1-k^2*x)))))
%Y Cf. A256016, A357194.
%Y Cf. A352983, A357191.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Sep 17 2022
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