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A058808 Product{k=1 to n}[S(n,k)], where S(n,k) is a Stirling number of the second kind. (S(n,k) = number of ways of partitioning a set of n elements into k nonempty subsets.)

%I A058808 #25 Feb 27 2021 07:38:02
%S A058808 1,1,3,42,3750,2720250,19512927000,1631977354072800,
%T A058808 1833446251541145780000,31323109023670061678062500000,
%U A058808 9087660958278168844264470405352500000
%N A058808 Product{k=1 to n}[S(n,k)], where S(n,k) is a Stirling number of the second kind. (S(n,k) = number of ways of partitioning a set of n elements into k nonempty subsets.)
%H A058808 Vaclav Kotesovec, <a href="/A058808/b058808.txt">Table of n, a(n) for n = 1..40</a>
%F A058808 log(a(n)) ~ n^2 * (log(n) + gamma - 3/2) / 2, where gamma is the Euler-Mascheroni constant A001620. - _Vaclav Kotesovec_, Feb 27 2021
%e A058808 a(4) = S(4,1)*S(4,2)*S(4,3)*S(4,4) = 1*7*6*1 = 42.
%p A058808 a:=n->mul(stirling2(n, k), k=1..n): seq(a(n), n=1..12); # _Zerinvary Lajos_, Jun 28 2007
%t A058808 Table[Product[StirlingS2[n, k], {k, 1, n}], {n, 1, 12}] (* _Vaclav Kotesovec_, Feb 26 2021 *)
%o A058808 (PARI) a(n) = prod(k=1, n, stirling(n, k, 2)); \\ _Michel Marcus_, Dec 12 2015
%Y A058808 Cf. A058807, A294373.
%K A058808 easy,nonn
%O A058808 1,3
%A A058808 _Leroy Quet_, Jan 02 2001