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%I #13 Jun 17 2024 09:58:38
%S 1,0,0,0,0,1,6,42,336,3024,30366,335412,4041576,52756704,741620880,
%T 11169844686,179448036768,3063069801792,55360031126400,
%U 1056123043335360,21208345049147256,447183762148547424,9877939209960101280,228112734232663600320
%N Expansion of e.g.f. exp(x^5/(120 * (1-x))).
%F a(n) = 2*(n-1) * a(n-1) - (n-1)*(n-2) * a(n-2) + binomial(n-1,4) * a(n-5) - 4*binomial(n-1,5) * a(n-6) for n > 5.
%F From _Seiichi Manyama_, Jun 17 2024: (Start)
%F a(n) = n! * Sum_{k=0..floor(n/5)} binomial(n-4*k-1,n-5*k)/(120^k * k!).
%F a(0) = 1; a(n) = ((n-1)!/120) * Sum_{k=5..n} k * a(n-k)/(n-k)!. (End)
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^5/(120*(1-x)))))
%Y Cf. A185369, A361533, A361545.
%K nonn
%O 0,7
%A _Seiichi Manyama_, Mar 15 2023
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