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%I #12 Jul 09 2022 11:05:24
%S 1,0,2,-3,32,-150,1404,-11340,120448,-1319976,16600320,-223664760,
%T 3300331704,-52223268240,887583503520,-16071609481200,309263446333440,
%U -6296705309543040,135262191966465600,-3056359409652695040,72462969268541596800
%N Expansion of e.g.f. exp(f(x) - 1) where f(x) = (1 + x)^x = e.g.f. for A007113.
%F a(0) = 1; a(n) = Sum_{k=1..n} A007113(k) * binomial(n-1,k-1) * a(n-k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((1+x)^x-1)))
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j!*sum(k=0, j\2, stirling(j-k, k, 1)/(j-k)!)*binomial(i-1, j-1)*v[i-j+1])); v;
%Y Cf. A007113, A202152, A354613.
%K sign
%O 0,3
%A _Seiichi Manyama_, Jul 08 2022