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Expansion of e.g.f. exp( Sum_{k>=1} (3*k)! * (x/6)^k/k ).
2

%I #9 Feb 09 2024 01:48:40

%S 1,1,21,3421,2232361,4047831801,16492042429501,131524059703672021,

%T 1862832637043775536721,43582296764832433769579761,

%U 1592318494850388661944336320101,86870590496672779178378519636679501,6822481321458299127004125050236325798521

%N Expansion of e.g.f. exp( Sum_{k>=1} (3*k)! * (x/6)^k/k ).

%F a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} (3*k)! * a(n-k) / (6^k * (n-k)!).

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, (3*k)!*(x/6)^k/k))))

%Y Cf. A158876, A370084.

%Y Cf. A370087.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 08 2024