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 A200660 #37 Dec 11 2023 08:27:37
%S A200660 0,1,8,49,284,1658,9974,62375,406832,2769493,19668054,145559632,
%T A200660 1121153604,8974604065,74553168520,641808575961,5718014325296,
%U A200660 52653303354906,500515404889978,4905937052293759,49530189989912312,514541524981377909,5494885265473192914
%N A200660 Sum of the number of arcs describing the set partitions of {1,2,...,n}.
%C A200660 Supercharacter theory of unipotent upper triangular matrices over a finite field F(2) is indexed by set partitions S(n) of {1,2,...,n} where a set partition P of {1,2,...,n} is a subset { (i,j) : 1 <= i < j <= n} such that (i,j) in P implies (i,k),(k,j) are not in P for all i < l < j.
%C A200660 One of the statistics used to compute the supercharacter table is the number of arcs in P (that is, the cardinality |P| of P).
%C A200660 The sequence we have is arcs(n) = Sum_{P in S(n)} |P|.
%H A200660 Seiichi Manyama, <a href="/A200660/b200660.txt">Table of n, a(n) for n = 1..500</a>
%H A200660 M. Aguiar, C. Andre, C. Benedetti, N. Bergeron, Z. Chen, P. Diaconis, A. Hendrickson, S. Hsiao, I. M. Isaacs, A. Jedwab, K. Johnson, G. Karaali, A. Lauve, T. Le, S. Lewis, H. Li, K. Magaard, E. Marberg, J-C. Novelli, A. Pang, F. Saliola, L. Tevlin, J-Y. Thibon, N. Thiem, V. Venkateswaran, C. R. Vinroot, N. Yan, and M. Zabrocki, <a href="http://arxiv.org/abs/1009.4134">Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras</a>, arXiv:1009.4134 [math.CO], 2010-2011.
%H A200660 C. André, <a href="https://doi.org/10.1006/jabr.2001.8734">Basic characters of the unitriangular group</a>, Journal of Algebra, 175 (1995), 287-319.
%F A200660 a(n) = Sum_{k=1..n} Stirling2(n,k) * k * (n-k). - _Ilya Gutkovskiy_, Apr 06 2021
%F A200660 a(n) = Sum_{k=n..n*(n+1)/2} (k-n) * A367955(n,k). - _Alois P. Heinz_, Dec 11 2023
%p A200660 b:=proc(n,k) option remember;
%p A200660 if n=1 and k=1 then RETURN(1) fi;
%p A200660 if k=1 then RETURN(b(n-1,n-1)) fi;
%p A200660 b(n,k-1)+b(n-1,k-1)
%p A200660 end:
%p A200660 arcs:=proc(n) local res,k;
%p A200660 res:=0;
%p A200660 for k to n-1 do res:=res+ k*b(n,k) od;
%p A200660 res
%p A200660 end:
%p A200660 seq(arcs(n),n=1..34);
%t A200660 b[n_, k_] := b[n, k] = Which[n == 1 && k == 1, 1, k == 1, b[n - 1, n - 1], True, b[n, k - 1] + b[n - 1, k - 1]];
%t A200660 arcs[n_] := Module[{res = 0, k}, For[k = 1, k <= n-1, k++, res = res + k * b[n, k]]; res];
%t A200660 Array[arcs, 34] (* _Jean-François Alcover_, Nov 25 2017, translated from Maple *)
%Y A200660 Cf. A011971 (sequence is computed from Aitken's array b(n,k) arcs(n) = Sum_{k=1..n-1} k*b(n,k)).
%Y A200660 Cf. A200580, A200673 (other statistics related to supercharacter table).
%Y A200660 Cf. A367955.
%K A200660 nonn
%O A200660 1,3
%A A200660 _Nantel Bergeron_, Nov 20 2011