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 A361829 #14 Mar 26 2023 10:25:20
%S A361829 1,2,10,62,486,4482,47106,553226,7152438,100644194,1527758136,
%T A361829 24839853326,430045385424,7888706328934,152685931935634,
%U A361829 3106864307092950,66253232332628166,1476558925897693698,34307420366092350048,829217371825336147142
%N A361829 a(n) = Sum_{k=0..n} binomial(2*k,k) * binomial(n*k,n-k).
%F A361829 a(n) = [x^n] 1/sqrt(1 - 4*x*(1+x)^n).
%F A361829 log(a(n)) ~ n*(log(n) + (2*log(2) - 1)/log(n) - (1 - 1/log(n))*log(log(n) - 1)). - _Vaclav Kotesovec_, Mar 26 2023
%t A361829 Table[Sum[Binomial[2*k,k]*Binomial[n*k,n-k], {k,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Mar 26 2023 *)
%o A361829 (PARI) a(n) = sum(k=0, n, binomial(2*k, k)*binomial(n*k, n-k));
%Y A361829 Main diagonal of A361830.
%Y A361829 Cf. A099237, A361835.
%K A361829 nonn
%O A361829 0,2
%A A361829 _Seiichi Manyama_, Mar 26 2023