OFFSET
7,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 7..10000 (terms n = 5001..9000 from Vaclav Kotesovec)
Wikipedia, Partition (number theory)
FORMULA
a(n) ~ exp(Pi*sqrt(7*n/3)) * 7^(1/4) / (32 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 16 2019
G.f.: (-1 + Product_{k>=1} (1 + x^k))^7. - Ilya Gutkovskiy, Jan 31 2021
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add((t->
b(t, min(t, i-1), k)*binomial(k, j))(n-i*j), j=0..min(k, n/i))))
end:
a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(7):
seq(a(n), n=7..45);
MATHEMATICA
A327385[n_] := SeriesCoefficient[(Product[(1 + x^k), {k, 1, n}] - 1)^7, {x, 0, n}]; Table[A327385[n], {n, 7, 37}] (* Robert P. P. McKone, Jan 31 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 03 2019
STATUS
approved