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%I #9 Nov 20 2020 21:38:12
%S 1,0,0,0,0,2,2,2,2,2,506,1850,5018,12014,26886,1066782,8193070,
%T 42723722,185108514,719359762,10426744914,118490840686,976376930502,
%U 6583701431086,38977418758494,377188932759354,4671829781287922,51479602726372402,483303800325691922
%N E.g.f.: exp(2 * (exp(x) - 1 - x - x^2 / 2 - x^3 / 6 - x^4 / 24)).
%H Seiichi Manyama, <a href="/A339027/b339027.txt">Table of n, a(n) for n = 0..576</a>
%F a(0) = 1; a(n) = 2 * Sum_{k=5..n} binomial(n-1,k-1) * a(n-k).
%F a(n) = Sum_{k=0..n} binomial(n,k) * A057814(k) * A057814(n-k).
%t nmax = 28; CoefficientList[Series[Exp[2 (Exp[x] - 1 - x - x^2/2 - x^3/6 - x^4/24)], {x, 0, nmax}], x] Range[0, nmax]!
%t a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[n - 1, k - 1] a[n - k], {k, 5, n}]; Table[a[n], {n, 0, 28}]
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(2 * (exp(x) - 1 - x - x^2/2 - x^3/6 - x^4/24)))) \\ _Michel Marcus_, Nov 20 2020
%Y Cf. A001861, A057814, A194689, A339014, A339017.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Nov 20 2020
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