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 A370212 #11 Feb 12 2024 08:38:43
%S A370212 1,1,1,4,17,51,142,442,1457,4702,14951,48038,156158,508860,1658112,
%T A370212 5414754,17735473,58209803,191310964,629605300,2074916167,6846553375,
%U A370212 22615507300,74775856026,247463508542,819645776926,2716912851446,9012261102106,29914317146864
%N A370212 Coefficient of x^n in the expansion of ( (1+x) / (1-x^3) )^n.
%F A370212 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(n,n-3*k).
%F A370212 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / (1+x) * (1-x^3) ). See A215340.
%o A370212 (PARI) a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial(u*n, n-s*k));
%Y A370212 Cf. A215340.
%K A370212 nonn
%O A370212 0,4
%A A370212 _Seiichi Manyama_, Feb 12 2024