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 A378464 #7 Nov 27 2024 08:06:31
%S A378464 1,1,3,13,63,306,1473,7085,34239,166459,813618,3994200,19678233,
%T A378464 97239130,481740885,2392004853,11900655999,59312062026,296071376307,
%U A378464 1479998924447,7407613846698,37118966710076,186195636158436,934889598483048,4698229684691913,23629859054461331
%N A378464 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(2*n-1,n-3*k).
%F A378464 a(n) = [x^n] 1/(1 - x - x^3/(1 - x)^2)^n.
%o A378464 (PARI) a(n) = sum(k=0, n\3, binomial(n+k-1, k)*binomial(2*n-1, n-3*k));
%Y A378464 Cf. A370624, A378463.
%Y A378464 Cf. A367413.
%K A378464 nonn
%O A378464 0,3
%A A378464 _Seiichi Manyama_, Nov 27 2024