max = 61; 

(*** A000598 ***)
G000598 = 0;
i = 0;
While[ i < max+1, 
  G000598 = Series[1+z*(G000598^3/6+
	(G000598 /. z->z^2)*G000598/2+
	(G000598 /. z->z^3)/3),{z,0,max+1}] // Normal;
  t[i] = G000598; 
  i = i+1
];
A000598[n_] := Coefficient[G000598,z,n]; 
For[ n = 0, n <= max-1, n++, Print[{n, A000598[n]}]]; 


(*** A000678 ***)
i = 0;
While[ i < max+1, 
  T = t[i];
  G000678 = Series[z*(T^4/24+(T/.z->z^2)*T^2/4+
	(T/.z->z^2)^2/8+T*(T/.z->z^3)/3+
	(T/.z->z^4)/4),{z,0,max+1}]//Normal;
  q[i] = G000678;
  i = i+1
];
A000678[n_] := Coefficient[G000678,z,n]; 
For[ n = 0, n <= max-1, n++, Print[{n, A000678[n]}]]; 


(*** A000022 ***)
i = 1;
While[ i < max+1, 
  Tb = t[i]-t[i-1];
  Ts = t[i]-1;
  Q2 = Series[Tb*Ts,{z,0,200}]//Normal;
  q2[i] = Q2;
  i = i+1
];
q2[0] = 0;
q[-1] = 0;
For[ i = 0, i <= max , i++,
  c[i] = Series[q[i]-q[i-1]-q2[i],{z,0,200}] // Normal
];
cent = Series[Sum[c[i],{i,0,max}],{z,0,200}] // Normal;
G000022 = cent;
A000022[n_] := Coefficient[G000022,z,n]; 
For[ n = 0, n <= max-1, n++, Print[{n, A000022[n]}]];


(*** A000200 ***)
For[ i = 1, i <= max ,i++, 
  tt = t[i]-t[i-1];
  b[i] = Series[(tt^2+( tt/.z->z^2))/2,{z,0,200}] // Normal
]; 
bicent = Series[Sum[b[i],{i,1,max}],{z,0,200}] // Normal;
G000200 = bicent;
A000200[n_] := Coefficient[G000200,z,n]; 
For[ n = 0, n <= max-1, n++, Print[{n, A000200[n]}]];


(*** A000602 ***)
A000602[n_] := If[n==0, Return[1], A000022[n]+A000200[n]];
For[ n = 0, n <= max-1, n++, Print[{n, A000602[n]}]];