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%I #10 Nov 13 2022 04:41:27
%S 1,1,2,9,48,315,2520,23415,248640,2972025,39463200,576413145,
%T 9184855680,158550787395,2947473809280,58707685211175,
%U 1247293022976000,28156003910859825,672972205556851200,16978695795089253225,450907982644863744000,12573634144960773960075
%N Expansion of e.g.f. 1/(1 - x * exp(x^2/2)).
%F a(n) = n! * Sum_{k=0..floor(n/2)} (n - 2*k)^k/(2^k * k!).
%F a(n) ~ n! / ((1 + LambertW(1)) * LambertW(1)^(n/2)). - _Vaclav Kotesovec_, Nov 13 2022
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^2/2))))
%o (PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*k!));
%Y Cf. A006153, A358265.
%Y Cf. A354550, A358064.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Nov 06 2022
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