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G.f. A(x) satisfies: 1+x = A(xA(2xA(3xA(4xA(...(n*xA(...))))))).
0

%I #3 Mar 30 2012 18:36:39

%S 1,1,-2,10,-80,1000,-21872,977584,-96293648,20624493808,

%T -9328274380160,8744603171127040,-16802076392609925440,

%U 65695424926762378460992,-520141011157056880989068672

%N G.f. A(x) satisfies: 1+x = A(xA(2xA(3xA(4xA(...(n*xA(...))))))).

%e A(xA(2xA(3xA(4x)))) = 1 + x - 120x^5 + 5280x^6 - 192000x^7 +-...

%e A(xA(2xA(3xA(4xA(5x))))) = 1 + x - 720x^6 + 46800x^7 - 2332800x^8 +-...

%e A(xA(2xA(...(n-2)xA((n-1)x)))) = 1 + x - n!x^n + (n-1)(2n+1)n!x^(n+1) -+...

%K sign

%O 0,3

%A _Paul D. Hanna_, Sep 26 2003