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A353344 Expansion of e.g.f. exp(-log(1 - x)^3).

%I A353344 #19 Oct 19 2022 11:11:45
%S A353344 1,0,0,6,36,210,1710,17304,194712,2402184,32536080,481094856,
%T A353344 7703580456,132658888752,2443228469136,47904722262144,995970495769920,
%U A353344 21879712141853760,506301721998264000,12306713585213260800,313441368701926135680,8345931596469584686080
%N A353344 Expansion of e.g.f. exp(-log(1 - x)^3).
%H A353344 Seiichi Manyama, <a href="/A353344/b353344.txt">Table of n, a(n) for n = 0..442</a>
%F A353344 E.g.f.: (1 - x)^(-(log(1 - x))^2).
%F A353344 a(0) = 1; a(n) = 6 * Sum_{k=1..n} binomial(n-1,k-1) * |Stirling1(k,3)| * a(n-k).
%F A353344 a(n) = Sum_{k=0..floor(n/3)} (3*k)! * |Stirling1(n,3*k)|/k!.
%o A353344 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-log(1-x)^3)))
%o A353344 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x)^(-log(1-x)^2)))
%o A353344 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=6*sum(j=1, i, binomial(i-1, j-1)*abs(stirling(j, 3, 1))*v[i-j+1])); v;
%o A353344 (PARI) a(n) = sum(k=0, n\3, (3*k)!*abs(stirling(n, 3*k, 1))/k!);
%Y A353344 Column k=3 of A357882.
%Y A353344 Cf. A000142, A353358, A353404.
%Y A353344 Cf. A347002, A353118, A353664.
%K A353344 nonn
%O A353344 0,4
%A A353344 _Seiichi Manyama_, May 06 2022