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A036717 G.f. satisfies A(x) = 1 + x*cycle_index(Alt(4), A(x)). 22

%I #9 Jan 16 2013 10:07:38

%S 1,1,1,2,4,9,19,47,113,287,733,1920,5064,13557,36553,99455,272293,

%T 750262,2077751,5781971,16156866,45321635,127566689,360191846,

%U 1019926954,2895648896,8240832570,23505344031,67183161970,192393195097,551946691853

%N G.f. satisfies A(x) = 1 + x*cycle_index(Alt(4), A(x)).

%p A := 1; f := proc(n) global A; local A2,A3; A2 := subs(x=x^2,A); A3 := subs(x=x^3,A);

%p coeff(series( 1+x*( (A^4+3*A2^2+8*A*A3)/12), x, n+1), x,n); end;

%p for n from 1 to 50 do A := series(A+f(n)*x^n,x,n +1); od: A;

%t a = 1; f[n_] := Module[{a2, a3}, a2 = a /. x -> x^2; a3 = a /. x -> x^3; Coefficient[ Series[1 + x*(a^4 + 3*a2^2 + 8*a*a3)/12, {x, 0, n + 1}] // Normal, x, n]]; For[n = 1, n <= 30, n++, a = Series[a + f[n]*x^n, {x, 0, n + 1}] // Normal]; CoefficientList[a, x] (* _Jean-François Alcover_, Jan 16 2013, after Maple *)

%K nonn

%O 0,4

%A _N. J. A. Sloane_.

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