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Expansion of e.g.f. exp( x * (exp(x^2) - 1) ).
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%I #14 Oct 22 2022 14:02:14

%S 1,0,0,6,0,60,360,840,20160,75600,1058400,10311840,79833600,

%T 1305944640,11018367360,174616041600,2150397849600,28661419987200,

%U 473667677683200,6293779652160000,114484773731328000,1766543101087564800,31640707215390873600

%N Expansion of e.g.f. exp( x * (exp(x^2) - 1) ).

%F a(n) = n! * Sum_{k=0..floor(n/2)} Stirling2(k,n-2*k)/k!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2)-1))))

%o (PARI) a(n) = n!*sum(k=0, n\2, stirling(k, n-2*k, 2)/k!);

%Y Cf. A357967, A357968.

%Y Cf. A353226.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Oct 22 2022