%I #2 Mar 30 2012 18:37:21

%S 1,1,-3,11,-49,134,-1915,-30437,-1176925,-47572678,-2240962254,

%T -119077789557,-7053073003902,-460586576005843,-32870527083358387,

%U -2544978866143616029,-212452025172991768237,-19021387591827001945347

%N G.f. satisfies: [x^n] A(x)^((n+1)^2) = (n+1)^2 for n>=1; that is, the coefficient of x^n in the (n+1)^2 power of g.f. A(x) equals (n+1)^2.

%e G.f.: A(x) = 1 + x - 3*x^2 + 11*x^3 - 49*x^4 + 134*x^5 - 1915*x^6 +...

%e Coefficients in the squared powers of A(x) begin:

%e A(x)^1: [(1), 1, -3, 11, -49, 134, -1915, -30437, ...];

%e A(x)^4: [1, (4), -6, 12, -45, -220, -4952, -148944, ...];

%e A(x)^9: [1, 9, (9), -33, 45, -1044, -13353, -387675, ...];

%e A(x)^16: [1, 16, 72, (16), -284, -1408, -36152, -857136, ...];

%e A(x)^25: [1, 25, 225, 775, (25), -6520, -78725, -1861575, ...];

%e A(x)^36: [1, 36, 522, 3756, 12411, (36), -229128, -4096368, ...];

%e A(x)^49: [1, 49, 1029, 11907, 80115, 283514, (49), -10015593, ...];

%e A(x)^64: [1, 64, 1824, 30272, 319760, 2177792, 8628896, (64), ...]; ...

%e where the coefficients [x^n] A(x)^((n+1)^2) form the squares.

%o (PARI) {a(n)=local(A=[1,1]);for(m=3,n+1,A=concat(A,0);A[ #A]=(m^2-Vec(Ser(A)^(m^2))[m])/m^2);A[n+1]}

%K sign

%O 0,3

%A _Paul D. Hanna_, Feb 02 2010