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 A370390 #21 Feb 18 2024 18:53:42
%S A370390 0,0,1,2,10,53,334,2428,20009,184440,1881050,21034905,255967940,
%T A370390 3367720736,47641219569,721160081974,11631770791362,199159952915293,
%U A370390 3607908007376418,68946510671942892,1386140583681969289,29247292475233307612,646231776371742321826
%N A370390 Number of permutations of [n] whose longest block is of length 2. A block of a permutation is a maximal sequence of consecutive integers which appear in consecutive positions.
%H A370390 Alois P. Heinz, <a href="/A370390/b370390.txt">Table of n, a(n) for n = 0..450</a>
%F A370390 a(n) = A002628(n) - A000255(n-1).
%F A370390 G.f.: Sum_{k>=0} k! * x^k * ( ((1-x^2)/(1-x^3))^k - ((1-x)/(1-x^2))^k ).
%o A370390 (PARI) my(N=30, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, N, k!*x^k*(((1-x^2)/(1-x^3))^k-((1-x)/(1-x^2))^k))))
%Y A370390 Column k=2 of A184182.
%Y A370390 Cf. A000255, A002628.
%K A370390 nonn
%O A370390 0,4
%A A370390 _Seiichi Manyama_, Feb 17 2024