This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A023997 #27 Aug 31 2023 10:49:43
%S A023997 1,1,3,25,339,6721,179643,6166105,262308819,13471274401,818288740923,
%T A023997 57836113793305,4693153430067699,432360767273547841,
%U A023997 44794795522199781243,5176959027946049635225,662704551840482536170579
%N A023997 Number of block permutations on an n-set.
%C A023997 A block permutation of a set X is a bijection between two quotient sets of X (of necessarily equal rank).
%C A023997 Number of labeled partitions of (n,n) into pairs (i,j) where there are n black objects labeled 1..n and n white objects labeled 1..n. Each partition must have at least one black object and at least one white object. - _Christian G. Bower_, Jun 03 2005
%H A023997 Vaclav Kotesovec, <a href="/A023997/b023997.txt">Table of n, a(n) for n = 0..288</a> (terms 0..45 from Vincenzo Librandi)
%H A023997 Zhanar Berikkyzy, Pamela E. Harris, Anna Pun, Catherine Yan, and Chenchen Zhao, <a href="https://arxiv.org/abs/2308.14183">Combinatorial Identities for Vacillating Tableaux</a>, arXiv:2308.14183 [math.CO], 2023. See p. 22.
%H A023997 D. G. FitzGerald and Jonathan Leech, <a href="https://doi.org/10.1017/S1446788700039227">Dual symmetric inverse monoids and representation theory</a>, J. Australian Mathematical Society (Series A), Vol. 64 (1998), pp. 345-367.
%F A023997 a(0)=1, a(n) = Sum_{k=1..n} k! * S2(n,k)^2, S2(n,k) are the Stirling numbers of the second kind.
%e A023997 For n=3, there are the 3! ordinary permutations (of rank 3), 18 block permutations of rank 2 (2! for each pair of partitions of rank 2) and the single rank 1 one.
%t A023997 Table[Sum[StirlingS2[n,k]^2k!,{k,0,n}],{n,0,100}] (* _Emanuele Munarini_, Jul 04 2011 *)
%o A023997 (Maxima) makelist(sum(stirling2(n,k)^2*k!,k,0,n),n,0,24); /* _Emanuele Munarini_, Jul 04 2011 */
%o A023997 (PARI) a(n) = if (n==0, 1, sum(k=1, n, k!*stirling(n, k, 2)^2)); \\ _Michel Marcus_, Jun 18 2019
%Y A023997 Cf. A023998, A002720, A014235, A111420.
%K A023997 easy,nonn,nice
%O A023997 0,3
%A A023997 Des FitzGerald (D.FitzGerald(AT)utas.edu.au)
%E A023997 More terms from _Christian G. Bower_, Jun 03 2005