OFFSET
7,3
FORMULA
G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^7.
MAPLE
g:= proc(n) option remember; `if`(n=0, 1, add(add([0, d, -d, d]
[1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
end:
b:= proc(n, k) option remember; `if`(k<2, `if`(n=0, 1-k, g(n)),
(q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2)))
end:
a:= n-> b(n, 7):
seq(a(n), n=7..44); # Alois P. Heinz, Feb 07 2021
MATHEMATICA
nmax = 44; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^7, {x, 0, nmax}], x] // Drop[#, 7] &
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 07 2021
STATUS
approved