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 A135312 #20 Dec 20 2024 08:16:49
%S A135312 1,1,4,13,62,311,1822,11593,80964,608833,4910786,42159239,383478988,
%T A135312 3678859159,37087880754,391641822541,4319860660448,49647399946049,
%U A135312 593217470459314,7354718987639959,94445777492433516,1254196823154143191,17198114810490326714,243191242578584519333
%N A135312 Number of transitive reflexive binary relations R on n labeled elements where |{y : xRy}| <= 2 for all x.
%D A135312 A. P. Heinz (1990). Analyse der Grenzen und Möglichkeiten schneller Tableauoptimierung. PhD Thesis, Albert-Ludwigs-Universität Freiburg, Freiburg i. Br., Germany.
%H A135312 Alois P. Heinz, <a href="/A135312/b135312.txt">Table of n, a(n) for n = 0..200</a>
%F A135312 a(n) = Sum_{i=0..floor(n/2)} C(n,2*i) * A006882(2*i-1) * A000248(n-2*i).
%F A135312 a(n) = A135302(n,2).
%F A135312 E.g.f.: exp(x*exp(x) + x^2/2).
%e A135312 a(2) = 4 because there are 4 relations of the given kind for 2 elements: 1R1, 2R2; 1R1, 2R2, 1R2; 1R1, 2R2, 2R1; 1R1, 2R2, 1R2, 2R1.
%p A135312 u:= proc(n) option remember; add(binomial(n, i)*(n-i)^i, i=0..n) end:
%p A135312 a:= n-> add(binomial(n, 2*i)*doublefactorial(2*i-1)*u(n-2*i), i=0..iquo(n, 2)):
%p A135312 seq(a(n), n=0..50);
%t A135312 a[n_] := SeriesCoefficient[Exp[x*Exp[x] + x^2/2], {x, 0, n}]*n!; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Feb 04 2014 *)
%Y A135312 Column k=2 of A135302.
%Y A135312 Cf. A006882, A000248, A007318.
%K A135312 nonn
%O A135312 0,3
%A A135312 _Alois P. Heinz_, Dec 05 2007