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 A383524 #11 Aug 30 2025 10:58:19
%S A383524 1,1,3,13,43,171,711,2913,12363,53203,230593,1010703,4463119,19827679,
%T A383524 88594299,397741893,1793063883,8113429419,36832823289,167701920759,
%U A383524 765577205433,3503296744233,16065995216109,73824301464939,339844364816559,1567063753104471,7237078197034221
%N A383524 a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(n-k,k)^2.
%C A383524 Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) - x*y^2*z^2).
%t A383524 Table[Sum[Binomial[n,k] * Binomial[n-k,k]^2,{k,0,n}], {n,0,30}] (* _Vaclav Kotesovec_, Aug 30 2025 *)
%o A383524 (PARI) a(n) = sum(k=0, n\2, binomial(n, k)*binomial(n-k, k)^2);
%Y A383524 Cf. A000172, A181545, A275027.
%K A383524 nonn,changed
%O A383524 0,3
%A A383524 _Seiichi Manyama_, Apr 29 2025