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%I #9 Jun 23 2024 16:13:13
%S 1,1,2,6,28,190,1730,20068,287406,4971884,102082882,2450448780,
%T 67879395878,2145912460492,76704301481034,3075725307199340,
%U 137422311677357710,6800630226338490492,370741889753741467970,22155195508036869880684,1444764915198178824091590
%N a(n) = Sum_{j=0..n} p(n - j, j) where p(n, x) = Sum_{k=0..n} k! * abs(Stirling1(n, k)) * x^k.
%p p := n -> local k; add(k!*abs(Stirling1(n, k))*x^k, k = 0..n):
%p a := n -> local j; add(subs(x=j, p(n - j)), j = 0..n):
%p seq(a(n), n = 0..20);
%t p[n_][x_] := Sum[k!*Abs[StirlingS1[n, k]]*If[k == 0, 1, x^k], {k, 0, n}];
%t a[n_] := Sum[p[n - j][j], {j, 0, n}];
%t Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, May 12 2024 *)
%Y Cf. A372346, A372347, A372348.
%Y Cf. A225479.
%K nonn
%O 0,3
%A _Peter Luschny_, Apr 29 2024
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