OFFSET
40,7
LINKS
FORMULA
a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} [Omega(r) = Omega(q) = Omega(p) = Omega(o) = Omega(m) = Omega(l) = Omega(k) = Omega(j) = Omega(i) = Omega(n-i-j-k-l-m-o-p-q-r) = 2], where Omega is the number of prime factors with multiplicity (A001222) and [ ] is the (generalized) Iverson bracket.
a(n) = [x^n y^10] 1/Product_{j>=1} (1-y*x^A001358(j)). - Alois P. Heinz, May 19 2021
MAPLE
h:= proc(n) option remember; `if`(n=0, 0,
`if`(numtheory[bigomega](n)=2, n, h(n-1)))
end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
`if`(i>n, 0, x*b(n-i, h(min(n-i, i))))+b(n, h(i-1)))), x, 11)
end:
a:= n-> coeff(b(n, h(n)), x, 10):
seq(a(n), n=40..120); # Alois P. Heinz, May 26 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 13 2021
EXTENSIONS
a(83)-a(103) from Alois P. Heinz, May 18 2021
STATUS
approved