with(combinat):with(numtheory): 
M:=30;

for n from 1 to M do    # do 1

p:=partition(n); s:=0:

for k from 1 to nops(p) do    # do 2
# get next partition of n
ex:=1:
# discard if there is an even part
for i from 1 to nops(p[k]) do if p[k][i] mod 2=0 then ex:=0:break:fi: od:
# analyze an odd partition

if ex=1 then                        # if 3
# convert partition to list of sizes of parts
q:=convert(p[k],multiset); 
lprint("q = ",q);
for i from 1 to n do a(i):=0: od:
for i from 1 to nops(q) do a(q[i][1]):=q[i][2]: od:
lprint([seq(a(i),i=1..n)]);
# get number of parts
nump := add(a(i),i=1..n);
lprint("nump =", nump);

# get multiplicity 
c:=1: for i from 1 to n do c:=c*a(i)!*i^a(i): od: 
lprint("c =", c);

# get exponent t(j)
tj:=0;
   for i from 1 to n do for j from 1 to n do
if a(i)>0 and a(j)>0 then tj:=tj+a(i)*a(j)*gcd(i,j); fi;
   od: od:
lprint("tj =", tj);

# change the following minus sign to plus to get A093934
s:=s + (1/c)*2^((tj-nump)/2);

fi:                                  # fi 3

od;   # od 2

A[n]:=s;
od:   # od 1

[seq(A[n],n=1..M)];