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 A363582 #21 Jun 14 2023 12:12:07
%S A363582 1,2,3,6,12,22,44,88,169,338,676,1322,2644,5288,10433,20866,41732,
%T A363582 82736,165472,330944,658012,1316024,2632048,5242778,10485556,20971112,
%U A363582 41822049,83644098,167288196,333885702,667771404,1335542808,2667053601,5334107202,10668214404
%N A363582 Number of admissible mesa sets among Stirling permutations of order n.
%D A363582 Nicolle González, Pamela E. Harris, Gordon Rojas Kirby, Mariana Smit Vega Garcia, and Bridget Eileen Tenner, "Mesas of Stirling permutations," preprint.
%H A363582 Alois P. Heinz, <a href="/A363582/b363582.txt">Table of n, a(n) for n = 1..3323</a>
%F A363582 Let n = 3*k+r, where r is in {0,1,2}, and let C_(x,y) be the rational Catalan numbers (A328901/A328902). Then a(n) = 2^(n-1) - Sum_{i=0..k-1} 2^(3*i+r)*C_(2*(k-i)-1,k-i).
%e A363582 For n = 4, the a(4) = 6 admissible pinnacle sets for Stirling permutations of order 4 are {}, {2}, {3}, {4}, {2,4}, and {3,4}.
%p A363582 a:= proc(n) option remember; `if`(n<4, n, (2*n*(2*n-3)*
%p A363582 a(n-1)+27*(n-4)*(n-2)*(a(n-3)/2-a(n-4)))/(n*(2*n-3)))
%p A363582 end:
%p A363582 seq(a(n), n=1..45); # _Alois P. Heinz_, Jun 13 2023
%Y A363582 Cf. A289871, A359066, A359067, A328901, A328902.
%K A363582 nonn
%O A363582 1,2
%A A363582 _Bridget Tenner_, Jun 10 2023
%E A363582 More terms from _Alois P. Heinz_, Jun 13 2023