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%I #11 May 18 2022 13:12:55
%S 1,0,0,0,0,1,-15,175,-1960,22449,-269199,3410000,-45753180,650179816,
%T -9771920158,155020385156,-2589888417480,45461879164584,
%U -836540418765834,16099972965770778,-323385447259166454,6764948641797695496,-147088325599708573080
%N Expansion of e.g.f. exp(log(1 + x)^5/120).
%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * Stirling1(k,5) * a(n-k).
%F a(n) = Sum_{k=0..floor(n/5)} (5*k)! * Stirling1(n,5*k)/(120^k * k!).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(log(1+x)^5/120)))
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, binomial(i-1, j-1)*stirling(j, 5, 1)*v[i-j+1])); v;
%o (PARI) a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 1)/(120^k*k!));
%Y Cf. A354136.
%Y Cf. A327506, A347004, A354135.
%K sign
%O 0,7
%A _Seiichi Manyama_, May 18 2022
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