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 A383481 #16 May 28 2025 16:34:21
%S A383481 1,1,3,10,39,156,630,2556,10431,42823,176748,732810,3049722,12732188,
%T A383481 53299284,223645200,940355391,3961092906,16712516565,70615352330,
%U A383481 298761296064,1265504676810,5366250376710,22777466596560,96768003904650,411451657313931,1750809473690436,7455339422353396
%N A383481 Coefficient of x^n in the expansion of 1 / (1-x-x^4)^n.
%H A383481 Robert Israel, <a href="/A383481/b383481.txt">Table of n, a(n) for n = 0..1564</a>
%F A383481 a(n) = Sum_{k=0..floor(n/4)} binomial(n+k-1,k) * binomial(2*n-3*k-1,n-4*k).
%F A383481 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x-x^4) ).
%p A383481 f:= proc(n) local k; add(binomial(n+k-1,k)*binomial(2*n-3*k-1,n-4*k),k=0..n/4) end proc:
%p A383481 map(f, [$0..40]); # _Robert Israel_, May 28 2025
%o A383481 (PARI) a(n, s=4, t=1, u=0) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
%Y A383481 Cf. A003269, A063021, A370624.
%K A383481 nonn
%O A383481 0,3
%A A383481 _Seiichi Manyama_, Apr 28 2025