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A351515 Expansion of e.g.f. (exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)^2 / 2.

%I A351515 #12 Feb 13 2022 06:32:29
%S A351515 1,15,215,3325,56605,1060780,21772595,486459105,11760431325,
%T A351515 305942552245,8521928511915,253041654671949,7977871631560394,
%U A351515 266128899746035160,9363456107172891499,346487270686107589124,13450341325170239245308,546470289216642540029570
%N A351515 Expansion of e.g.f. (exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)^2 / 2.
%F A351515 a(n) = Sum_{k=1..n-1} binomial(n-1,k) * A000357(k) * A000357(n-k).
%o A351515 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((exp(exp(exp(exp(exp(x)-1)-1)-1)-1)-1)^2/2))
%o A351515 (PARI) T(n, k) = if(k==0, n<=1, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
%o A351515 a(n) = sum(k=1, n-1, binomial(n-1, k)*T(k, 5)*T(n-k, 5));
%Y A351515 Column 2 of A039813.
%Y A351515 Cf. A000357, A000558, A351513, A351514.
%K A351515 nonn
%O A351515 2,2
%A A351515 _Seiichi Manyama_, Feb 12 2022