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 A378612 #8 Dec 02 2024 10:09:41
%S A378612 1,3,27,264,2703,28443,304740,3306852,36225519,399755001,4437142467,
%T A378612 49485052224,554059164036,6224177431332,70120015345512,
%U A378612 791898021185484,8962485528377583,101626868754849381,1154295872365035537,13130360954151723480,149562006735075309783
%N A378612 a(n) = Sum_{k=0..n} binomial(3*n+k-1,k) * binomial(n-1,n-k).
%F A378612 a(n) = [x^n] 1/(1 - x/(1 - x))^(3*n).
%F A378612 a(n) = (1/4)^n * [x^(3*n)] 3/(1 - x/(1 - x))^n for n > 0.
%o A378612 (PARI) a(n) = sum(k=0, n, binomial(3*n+k-1, k)*binomial(n-1, n-k));
%Y A378612 Cf. A002002, A378611, A378613.
%Y A378612 Cf. A369012.
%K A378612 nonn
%O A378612 0,2
%A A378612 _Seiichi Manyama_, Dec 01 2024