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 A378463 #8 Nov 27 2024 08:06:37
%S A378463 1,1,3,13,59,266,1203,5489,25259,117022,545038,2549592,11970035,
%T A378463 56372460,266194295,1259910113,5975382699,28390616727,135108035502,
%U A378463 643891031826,3072604703774,14679493913048,70206875750168,336103001918788,1610476039036259,7723148579525441
%N A378463 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(2*n-k-1,n-3*k).
%F A378463 a(n) = [x^n] 1/(1 - x - x^3/(1 - x))^n.
%o A378463 (PARI) a(n) = sum(k=0, n\3, binomial(n+k-1, k)*binomial(2*n-k-1, n-3*k));
%Y A378463 Cf. A370624, A378464.
%Y A378463 Cf. A054515.
%K A378463 nonn
%O A378463 0,3
%A A378463 _Seiichi Manyama_, Nov 27 2024