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%I #2 Mar 30 2012 18:37:18
%S 1,1,2,20,804,108304,49833296,87606851264,641794234287360,
%T 19783636266156204928,2512584289692759254055168,
%U 1295158553795409705964052724736,2690610592205668589191756477437574144
%N a(n+1) equals the coefficient of x^n in the 2^(n-1)-th iteration of g.f. A(x) = Sum_{m>=1} a(m)*x^m for n>=1 with a(1)=1.
%e The coefficients of the 2^(n-1)-th iterations of the g.f. begin:
%e (1),1,2,20,804,108304,49833296,87606851264,641794234287360,...
%e 1,(2),6,51,1750,222706,100558052,175666197420,1284466715882828,...
%e 1,4,(20),170,4340,474238,204872756,353171251288,2572462315656538,...
%e 1,8,72,(804),15560,1128036,426923128,713954691088,5159170997828364,...
%e 1,16,272,5000,(108304),4271464,962562608,1461234395040,...
%e 1,32,1056,35856,1266720,(49833296),3774562656,3128786120000,...
%e 1,64,4160,273440,18169920,1226585248,(87606851264),12455033590400,...
%e 1,128,16512,2140224,278454400,36359377216,4771446963584,(641794234287360),...
%e in which the main diagonal forms this sequence shift left.
%o (PARI) {a(n)=local(F=x+x^2+sum(m=3, n-1, a(m)*x^m), G=x+x*O(x^n)); if(n<1, 0, if(n<=2, 1, for(i=1, n-1, G=subst(F, x, G);F=G); return(polcoeff(G, n-1, x))))}
%Y Cf. A119819.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Aug 10 2009