%I #3 Mar 31 2012 13:50:36
%S 1,1,0,2,0,0,5,0,0,0,8,5,0,0,0,19,20,0,0,0,0,66,55,1,0,0,0,0,280,48,
%T 64,0,0,0,0,0,645,584,35,22,0,0,0,0,0,2780,842,705,10,4,0,0,0,0,0,
%U 9163,2754,2867,30,46,0,0,0,0,0,0,29869,10771,9904,311,230,0,0,0,0,0,0,0
%N Let m = 3, 5, 7, ..., k = 0, 1, 2, 3, ..., z = (m+1)/2, 0 < j <= m. Let n_j be a prime number. Sequence gives T(m,k) = Table[m,k] = number of solutions to Sum_{d=1,2, ..., (z+k)}(n_j)_d = Sum_{d=1,2, ..., (z-k-1)}(n_j)_d = primorial number (A002110).
%F A022894(m) = Sum_{k=0, 1, 2, ..} [Number of solutions to Sum_{d=1, 2, ..., (z+k)}(n_j)_d = Sum_{ d=1, 2, ..., (z-k-1)}(n_j)_d]
%e {1}; {1,0}; {2,0,0}; {5,0,0,0}; {8,5,0,0,0}; {19,20,0,0,0,0}; ..... ->-> 3+2=5 {m=3, Table[3,0]=1}; 2+7+5=3+11 {m=5, Table[5,0]=1, Table[5,1]=0}; 17+2+7+3=13+5+11 and 2+11+3+13=17+7+5 {m=7, Table[7,0]=2, Table[7,1]=0, Table[7,2]=0}.
%Y Cf. A022894, A002110.
%K nonn,tabl
%O 0,4
%A _Naohiro Nomoto_, Nov 27 2000