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 A370426 #59 May 23 2025 04:16:19
%S A370426 0,0,0,0,1,3,9,48,306,2190,17810,162480,1642635,18231465,220420179,
%T A370426 2883693792,40592133316,611765693532,9828843229764,167702100599520,
%U A370426 3028466654021205,57708568527002415,1157199837194069405,24358905149602459920,537053113128448187766
%N A370426 Number of permutations of [n] having exactly two adjacent 2-cycles.
%H A370426 Seiichi Manyama, <a href="/A370426/b370426.txt">Table of n, a(n) for n = 0..452</a>
%H A370426 R. A. Brualdi and Emeric Deutsch, <a href="http://arxiv.org/abs/1005.0781">Adjacent q-cycles in permutations</a>, arXiv:1005.0781 [math.CO], 2010.
%F A370426 G.f.: (1/2) * Sum_{k>=2} k! * x^(k+2) / (1+x^2)^(k+1).
%F A370426 a(n) = (1/2) * Sum_{k=0..floor(n/2)-2} (-1)^k * (n-k-2)! / k!.
%F A370426 a(n) ~ n! / (2*n^2). - _Vaclav Kotesovec_, May 23 2025
%o A370426 (PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(sum(k=2, N, k!*x^(k+2)/(1+x^2)^(k+1))/2))
%o A370426 (PARI) a(n, k=2, q=2) = sum(j=0, n\q-k, (-1)^j*(n-(q-1)*(j+k))!/j!)/k!;
%Y A370426 Column k=2 of A177248.
%Y A370426 Cf. A177249, A370524, A370529.
%K A370426 nonn
%O A370426 0,6
%A A370426 _Seiichi Manyama_, Feb 21 2024