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 A378552 #14 Nov 30 2024 09:49:39
%S A378552 1,3,51,900,16455,307833,5850000,112445112,2180050215,42552000000,
%T A378552 835075676361,16461248223588,325696500000000,6464447754891285,
%U A378552 128654307202482420,2566472490000000000,51302899404879842343,1027391467409893403745,20607804108000000000000
%N A378552 a(n) = Sum_{k=0..n} 9^k * binomial(n/3+k-1,k) * binomial(n-1,n-k).
%F A378552 a(n) = [x^n] 1/(1 - 9*x/(1-x))^(n/3).
%t A378552 a[n_]:=SeriesCoefficient[1/(1 - 9*x/(1-x))^(n/3),{x,0,n}]; Array[a,19,0] (* _Stefano Spezia_, Nov 30 2024 *)
%o A378552 (PARI) a(n) = sum(k=0, n, 9^k*binomial(n/3+k-1, k)*binomial(n-1, n-k));
%Y A378552 Cf. A002002, A378551.
%Y A378552 Cf. A372110.
%K A378552 nonn
%O A378552 0,2
%A A378552 _Seiichi Manyama_, Nov 30 2024