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 A372499 #21 May 05 2024 08:54:44
%S A372499 0,1,6,9,54,0,-1944,44469,-323676,-5990193,179194032,484654509,
%T A372499 -105337511100,757846026261,85419734244300,-1707846638480514,
%U A372499 -90276038133498612,3464956887464464164,118426852966952180502,-7984363576091338944720,-181143285020960488524558
%N A372499 G.f. satisfies A(A(A(x))) = F(x), where F(x) is the g.f. for A053540(n) = n*9^(n-1).
%H A372499 Seiichi Manyama, <a href="/A372499/b372499.txt">Table of n, a(n) for n = 0..200</a>
%F A372499 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) = 1/3 * ( 9^(n-m) * binomial(n+m-1,2*m-1) - Sum_{l=m+1..n-1} (b(n,l) + Sum_{k=l..n} b(n,k) * b(k,l)) * b(l,m) ). a(n) = b(n,1).
%e A372499 A(A(x)) = x + 12*x^2 + 90*x^3 + 594*x^4 + 3807*x^5 + 20412*x^6 + 123201*x^7 + 1032264*x^8 - 1463103*x^9 - 35468766*x^10 + ...
%Y A372499 Cf. A309509, A372492.
%Y A372499 Cf. A053540, A141118, A372500.
%K A372499 sign
%O A372499 0,3
%A A372499 _Seiichi Manyama_, May 03 2024