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 A381482 #12 Apr 23 2025 10:55:22
%S A381482 1,1,9,37,241,1401,8961,57429,377217,2509201,16876729,114600069,
%T A381482 783903121,5397915433,37372017489,259998843477,1816376953857,
%U A381482 12736545070113,89602978644969,632223913939557,4472680961409201,31717890254271321,225416254500886689,1605197563027768917
%N A381482 a(n) = Sum_{k=0..floor(n/2)} binomial(n,k)^2 * binomial(n-k,k) * 2^k.
%C A381482 Diagonal of the rational function 1 / ((1 - x)*(1 - y)*(1 - z) - 2*x^2*y*z).
%F A381482 a(n) = hypergeom( [1/2 - n/2, -n, -n/2], [1, 1], -8).
%F A381482 a(n) ~ sqrt(7/12 + sqrt(89/38)*cosh(arccosh((8567*sqrt(19/178))/1424)/3)/3) * ((1/3 + 8*sqrt(7)*(cosh(arccosh(1261/(448*sqrt(7)))/3)/3))^n / Pi) / n. - _Vaclav Kotesovec_, Apr 23 2025
%t A381482 Table[Sum[Binomial[n, k]^2 Binomial[n - k, k] 2^k, {k, 0, Floor[n/2]}], {n, 0, 23}]
%t A381482 Table[HypergeometricPFQ[{1/2 - n/2, -n, -n/2}, {1, 1}, -8], {n, 0, 23}]
%Y A381482 Cf. A001045, A001850, A084601, A206178, A275027.
%K A381482 nonn
%O A381482 0,3
%A A381482 _Ilya Gutkovskiy_, Apr 22 2025