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

1, 1, 1, 2, 4, 9, 19, 47, 113, 287, 733, 1920, 5064, 13557, 36553, 99455, 272293, 750262, 2077751, 5781971, 16156866, 45321635, 127566689, 360191846, 1019926954, 2895648896, 8240832570, 23505344031, 67183161970, 192393195097, 551946691853

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Programs

Maple

A := 1; f := proc(n) global A; local A2,A3; A2 := subs(x=x^2,A); A3 := subs(x=x^3,A);
coeff(series( 1+x*( (A^4+3*A2^2+8*A*A3)/12), x, n+1), x,n); end;
for n from 1 to 50 do A := series(A+f(n)*x^n,x,n +1); od: A;

Mathematica

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 *)