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%I #43 Mar 06 2026 08:34:53
%S 1,1,6,36,280,2675,30216,394233,5835464,96627618,1769893080,
%T 35531597959,775839946464,18306267751369,464174851794094,
%U 12587054526203820,363493104803017184,11137369421602789775,360867894650798911704,12328474541846207359441,442905401932918535022500
%N a(0) = 1; a(n) = n * Sum_{k=1..n} binomial(n,k-1) * a(n-k).
%F G.f. A(x) satisfies: A(x) = 1 + x * d/dx ( x * A(x/(1 - x)) / (1 - x)^2 ).
%t a[0] = 1; a[n_] := a[n] = n Sum[Binomial[n, k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
%t nmax = 20; A[_] = 0; Do[A[x_] = 1 + x D[x A[x/(1 - x)]/(1 - x)^2, x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A006153, A040027, A367308.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Mar 05 2026