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 A372537 #18 May 05 2024 14:07:15
%S A372537 0,1,1,1,-15,81,-159,-1695,19857,-77775,-372351,6628545,-24096975,
%T A372537 -232640751,2756221601,2199811873,-210934282287,553408050417,
%U A372537 17722961332929,-95716389015423,-1950283855292559,15527782649242065,285278599792984545,-3006768595808218911
%N A372537 G.f. A(x) satisfies A(A(A(A(x)))) = x + 4*x^2 + 16*x^3.
%H A372537 Seiichi Manyama, <a href="/A372537/b372537.txt">Table of n, a(n) for n = 0..486</a>
%F A372537 Define the sequence b(n,m) as follows. If n<m, b(n,m) = 0, else if n=m, b(n,m) = 1, otherwise b(n,m) = 1/4 * ( 4^(n-m) * Sum_{l=0..m} binomial(l,n-3*m+2*l) * binomial(m,l) - Sum_{l=m+1..n-1} (b(n,l) + Sum_{k=l..n} (b(n,k) + Sum_{j=k..n} b(n,j) * b(j,k)) * b(k,l)) * b(l,m) ). a(n) = b(n,1).
%F A372537 Let B(x) = A(A(x)).
%F A372537 B(B(x)) = x + 4*x^2 + 16*x^3.
%F A372537 B(x) = F(2*x)/2, where F(x) is the g.f. for A220110.
%e A372537 A(A(x)) = x + 2*x^2 + 4*x^3 - 24*x^4 + 80*x^5 + 32*x^6 - 2496*x^7 + 14976*x^8 + ...
%Y A372537 Cf. A220110, A220288, A371841, A372521.
%K A372537 sign
%O A372537 0,5
%A A372537 _Seiichi Manyama_, May 05 2024