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%I #8 Jul 21 2023 07:48:15
%S 1,1,1,2,4,8,18,41,95,227,549,1344,3332,8332,21000,53310,136140,
%T 349536,901758,2336356,6076642,15860182,41527148,109048082,287119014,
%U 757829438,2004774538,5314615208,14116453336,37563744952,100126591704
%N Expansion of the solution of a functional equation.
%F Given g.f. A(x) and B(x) = g.f. of A112482, then B(x)=x+A(x*B(x)).
%F G.f. A(x)=y satisfies 0=y^3-y^2+(2x-1)y+x.
%F D-finite with recurrence 15*n*(n-1) *a(n) +(n-1)*(7*n-48) *a(n-1) +3*(-21*n^2 +99*n-118) *a(n-2) +(-151*n^2 +913*n-1362) *a(n-3) -80*(n-4) *(2*n-9) *a(n-4)=0. - _R. J. Mathar_, Jul 21 2023
%o (PARI) {a(n)=local(A); if(n<1, 0, A=O(x); for(k=1,n, A=A^3-A^2+2*x*A+x); polcoeff(A,n))}
%Y Cf. A112482.
%K nonn
%O 1,4
%A _Michael Somos_, Sep 08 2005
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