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 A363656 #30 Jun 14 2023 16:46:32
%S A363656 1,3,13,87,761,8243,106037,1578671,26685361,504770859,10562259533,
%T A363656 242216304839,6040459572681,162750100464643,4711225866217381,
%U A363656 145818462291970911,4805369568409107809,167982555421167341147,6208589923091273031293,241898639921607255506039
%N A363656 Number of bounded affine permutations of size n.
%C A363656 An affine permutation of size n is a bijection p from the integers to the integers that satisfies (1) p(i+n) = p(i) + n for all i and (2) Sum_{i=1..n} p(i) = Sum_{i=1..n} i. A bounded affine permutation of size n is an affine permutation of size n that satisfies (3) |p(i) - i| < n for all i.
%H A363656 Alois P. Heinz, <a href="/A363656/b363656.txt">Table of n, a(n) for n = 1..404</a>
%H A363656 N. Madras and J. M. Troyka, <a href="https://dmtcs.episciences.org/7302">Bounded affine permutations I. Pattern avoidance and enumeration</a>, Discrete Math. Theor. Comput. Sci. 22(2) (2021), #1.
%H A363656 N. Madras and J. M. Troyka, <a href="https://rdcu.be/czXKF">Bounded affine permutations II. Avoidance of decreasing patterns</a>, Ann. Comb. 25 (2021), 1007-1048.
%F A363656 a(n) = Sum_{m=0..n} binomial(n,m) Sum_{k=0..m} binomial(m,k) A046739(m,k) (Madras and Troyka I, Thm. 38(a)).
%F A363656 a(n) = Sum_{m=0..n} binomial(n,m) Sum_{k=0..m} binomial(m,n-k) (-1)^(n-m) A173018(m,k) (Madras and Troyka I, Thm. 38(b)).
%F A363656 a(n) ~ sqrt[3/(2*pi*e)] n^(-1/2) 2^n n! (Madras and Troyka I, Thm. 45).
%e A363656 Let [a,b] denote the affine permutation p of size 2 determined by p(1) = a and p(2) = b.
%e A363656 The 3 bounded affine permutations of size 2 are [1,2], [2,1], and [0,3], so a(2) = 3.
%Y A363656 Cf. A046739, A173018.
%K A363656 nonn
%O A363656 1,2
%A A363656 _Justin M. Troyka_, Jun 14 2023