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 A383280 #15 Apr 24 2025 04:22:44
%S A383280 1,2,9,72,954,19980,624510,27420120,1607036760,120942324720,
%T A383280 11351106055800,1298791163577600,177888712528573200,
%U A383280 28728740092874421600,5401708378739722249200,1169716267087957140552000,288993599402729842084464000,80796133625685147464322528000
%N A383280 a(n) = (3/2)^n * Sum_{k=0..n} (1/6)^k * (2*k)! * (n-k)! * binomial(n,k)^2.
%F A383280 a(n) = (n!)^2 * Sum_{k=0..n} (-1)^k * (3/2)^(n-k) * binomial(-1/2,k)/(n-k)!.
%F A383280 a(n) = (n!)^2 * [x^n] 1/sqrt(1-x) * exp(3*x/2).
%F A383280 a(n) = n * ( (n+1)*a(n-1) - 3*(n-1)^2/2 * a(n-2) ) for n > 1.
%F A383280 a(n) ~ 2 * sqrt(Pi) * n^(2*n + 1/2) / exp(2*n - 3/2). - _Vaclav Kotesovec_, Apr 24 2025
%o A383280 (PARI) a(n) = (3/2)^n*sum(k=0, n, (2*k)!*(n-k)!*binomial(n, k)^2/6^k);
%o A383280 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serlaplace(1/sqrt(1-x) * exp(3*x/2)))) \\ _Joerg Arndt_, Apr 22 2025
%Y A383280 Cf. A000681, A001499.
%K A383280 nonn
%O A383280 0,2
%A A383280 _Seiichi Manyama_, Apr 22 2025