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%I #10 Oct 08 2022 08:33:07
%S 0,1,2,6,32,220,1592,11944,96000,847120,8209952,86020704,958326272,
%T 11243157952,138464594816,1789358629504,24250275913728,
%U 344002396594432,5092763802452480,78443316497892864,1253887341918199808,20761127890765634560
%N Expansion of e.g.f. sinh( (exp(2*x) - 1)/sqrt(2) )/sqrt(2).
%F a(n) = Sum_{k=0..floor((n-1)/2)} 2^(n-1-k) * Stirling2(n,2*k+1).
%o (PARI) my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sinh((exp(2*x)-1)/sqrt(2))/sqrt(2)))))
%o (PARI) a(n) = sum(k=0, (n-1)\2, 2^(n-1-k)*stirling(n, 2*k+1, 2));
%Y Cf. A024429, A357665, A357666.
%Y Cf. A009599, A264037, A357661.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Oct 07 2022
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