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 A356114 #19 Aug 18 2022 09:18:17
%S A356114 0,0,0,2,9,24,55,118,245,500,1011,2034,4081,8176,16367,32750,65517,
%T A356114 131052,262123,524266,1048553,2097128,4194279,8388582,16777189,
%U A356114 33554404,67108835,134217698,268435425,536870880,1073741791,2147483614,4294967261,8589934556,17179869147
%N A356114 Number of irreducible permutations of n with partition type [2, 1, 1, ..., 1] (with '1' taken n - 2 times).
%C A356114 Irreducible permutations in connection with partition types are discussed in A356262. Compare with the subdiagonal of A356263.
%H A356114 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A356114 a(n) = 2^n - n - 3 for n >= 3.
%F A356114 a(n) = Eulerian1(n, n - 2) - 2 for n >= 3.
%F A356114 G.f.: x^3*(2*x^2 - x - 2)/((x - 1)^2*(2*x - 1)).
%F A356114 a(n) = A356263(n, n - 2) for n >= 2.
%e A356114 a(4) = 9 = card({2413, 2431, 3142, 3241, 3421, 4132, 4213, 4231, 4312}). The other two permutations of type [2, 1, 1], 1432 and 3214, are reducible. That there are 11 permutations of type [2, 1, 1] we know from Euler's triangle A173018 or from its refined form A355777.
%p A356114 seq(`if`(n < 3, 0, combinat:-eulerian1(n, n - 2) - 2), n = 0..34);
%Y A356114 Cf. A356262, A356263, A355777, A079500.
%K A356114 nonn,easy
%O A356114 0,4
%A A356114 _Peter Luschny_, Aug 01 2022