OFFSET
1,7
FORMULA
G.f.: (1/Product_{k>=1} (1-x^k)) * Sum_{k>=1} (-1)^(k-1) * x^(k*(3*k-1)/2) * (1-x^k) * (1+x^(7*k)) / (1-x^(7*k)).
MAPLE
b:= proc(n, i, c) option remember; `if`(i>n, 0, `if`(i=n,
`if`(irem(i-c, 7)=0, 1, 0), b(n-i, i, c+1)+b(n, i+1, c)))
end:
a:= n-> b(n, 1$2):
seq(a(n), n=1..55); # Alois P. Heinz, May 23 2023
PROG
(PARI) my(N=60, x='x+O('x^N)); Vec(1/prod(k=1, N, 1-x^k)*sum(k=1, N, (-1)^(k-1)*x^(k*(3*k-1)/2)*(1-x^k)*(1+x^(7*k))/(1-x^(7*k))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 23 2023
STATUS
approved