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 A381459 #18 May 12 2025 14:21:35
%S A381459 1,1,8,183,8320,628805,71172096,11266376947,2376282177536,
%T A381459 644092653605769,218152097885716480,90283850458537906511,
%U A381459 44828889635978905387008,26302150870235970074916493,18001952557737056033350615040,14215240470695667525160827723915
%N A381459 a(n) = (2*n)! * [x^(2*n)] cosh(x)^n.
%F A381459 a(n) = (1/2^n) * Sum_{k=0..n} (n-2*k)^(2*n) * binomial(n,k).
%F A381459 a(n) ~ c * ((1-2*r)^2 / (2 * r^r * (1-r)^(1-r)))^n * n^(2*n), where r = 0.015817782507793257357841601600685290637088885324182071456255... is the root of the equation (1-2*r)*(log(1-r) - log(r)) = 4 and c = 2*(1 - 2*r) / sqrt(1 + 4*r - 4*r^2) = 1.879106100687674868112932937483753439332007654254262530564... - _Vaclav Kotesovec_, May 11 2025, updated May 12 2025
%t A381459 Table[(2*n)! * SeriesCoefficient[Cosh[x]^n, {x, 0, 2*n}], {n, 0, 20}] (* _Vaclav Kotesovec_, May 11 2025 *)
%o A381459 (PARI) a(n) = sum(k=0, n, (n-2*k)^(2*n)*binomial(n, k))/2^n;
%Y A381459 Main diagonal of A326476.
%Y A381459 Cf. A242446.
%K A381459 nonn
%O A381459 0,3
%A A381459 _Seiichi Manyama_, May 11 2025