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 A369592 #14 Jun 20 2024 16:32:59
%S A369592 1,1,1,1,2,3,4,5,10,16,23,31,62,102,152,213,426,712,1084,1556,3112,
%T A369592 5255,8116,11843,23686,40288,62866,92842,185684,317548,499376,744277,
%U A369592 1488554,2556376,4044740,6072124,12144248,20926236,33272912,50244660,100489320,173634752
%N A369592 Expansion of (1/x) * Series_Reversion( x / (1+x+x^4/(1+x)^3) ).
%C A369592 Number of ordered trees with n+1 edges, having nonroot nodes of outdegree 0 or 4. - _Emanuele Munarini_, Jun 20 2024
%F A369592 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (n-4*k+1) * binomial(n+1,k).
%o A369592 (PARI) my(N=50, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^4/(1+x)^3))/x)
%o A369592 (PARI) a(n) = sum(k=0, n\4, (n-4*k+1)*binomial(n+1, k))/(n+1);
%Y A369592 Cf. A001405, A126042.
%Y A369592 Cf. A369525, A369581.
%K A369592 nonn
%O A369592 0,5
%A A369592 _Seiichi Manyama_, Jan 26 2024