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a(1) = 1; a(n) = Sum_{k=1..n-1} |Stirling1(n-1,k)|*a(k)*a(n-k).
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%I #6 Jul 25 2018 17:49:29

%S 1,1,2,9,97,3105,409318,301069244,1523141657289,61447697339843710,

%T 22299766257043761657829,80922067241038150103930448880,

%U 3230152742688615187688660954252643194,1547248455508510864175770056662224501358437847

%N a(1) = 1; a(n) = Sum_{k=1..n-1} |Stirling1(n-1,k)|*a(k)*a(n-k).

%t a[n_] := a[n] = Sum[Abs[StirlingS1[n - 1, k]] a[k] a[n - k], {k, n - 1}]; a[1] = 1; Table[a[n], {n, 14}]

%Y Cf. A008275, A137731, A143805.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Jul 25 2018