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%I #13 Jan 04 2024 08:57:27
%S 0,1,30,153,412,1065,1386,7105,-24072,275697,-2656970,29387721,
%T -352403820,4581620953,-64142155518,962133092145,-15394128425744,
%U 261700184657505,-4710603321945522,89501463119441017,-1790029262385620340,37590614510102111241
%N a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * k^5 / k!.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BellPolynomial.html">Bell Polynomial</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Touchard_polynomials">Touchard polynomials</a>
%F a(0) = 0; a(n) = -n*a(n-1) + n^5.
%F E.g.f.: B_5(x) * exp(x) / (1+x), where B_n(x) = Bell polynomials.
%o (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sum(k=0, 5, stirling(5, k, 2)*x^k)*exp(x)/(1+x))))
%Y Column k=5 of A368724.
%Y Cf. A048993, A368587, A368719.
%K sign
%O 0,3
%A _Seiichi Manyama_, Jan 04 2024
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