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%I #9 Jul 22 2024 00:49:14
%S 1,1,2,12,164,3780,128220,5962180,363377640,28109659104,2692076369460,
%T 312824482316588,43373419550214360,7074801917270302072,
%U 1341285553197404432856,292488135377674745120280
%N Sequence uniquely defined by: (n-1)*a(n) = n*[x^n] B(x) for n>1 with a(0)=a(1)=1, or, equivalently, 1+x - A(x) + x*A'(x) = x*B'(x), where B(x) = x/series_reversion(x*A(x)).
%C a(n) is divisible by n for n>0.
%F The g.f. of A120957 equals B(x) = x/series_reversion(x*A(x)), so that both A(x) = B(x*A(x)) and B(x) = A(x/B(x)) equivalently hold.
%o (PARI) {a(n)=my(A=[1,1]);if(n==0||n==1,1,for(i=1,n, A=concat(A,0);A[ #A]=(#A-2)*Vec(serreverse(x/Ser(A)))[ #A]);A[n+1]*n/(n-1))}
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 21 2006