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 A372413 #11 Apr 30 2024 06:08:11
%S A372413 1,0,0,3,4,5,21,49,92,237,595,1331,3169,7787,18487,44108,107036,
%T A372413 258349,622371,1508239,3658679,8869465,21543005,52399612,127497281,
%U A372413 310487855,756858661,1846060464,4505442967,11003284052,26887642756,65735882819,160795695676
%N A372413 Coefficient of x^n in the expansion of ( (1-x+x^3) / (1-x) )^n.
%F A372413 a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n-2*k-1,n-3*k).
%F A372413 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+x^3) ).
%o A372413 (PARI) a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
%Y A372413 Cf. A372414, A372415.
%Y A372413 Cf. A114997.
%K A372413 nonn
%O A372413 0,4
%A A372413 _Seiichi Manyama_, Apr 29 2024