OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1675
FORMULA
a(n) = [x^n] ((x^7-1)/(x-1))^n.
a(n) <= A088218(n) with equality only for n < 7.
From Peter Bala, Mar 31 2020: (Start)
a(n) = Sum_{i=0..n/7} (-1)^i*C(n,i)*C(2*n-7*i-1,n-7*i).
a(p) == 1 (mod p^2) for any prime p > 7.
More generally, we may have a(p^k) == a(p^(k-1)) (mod p^(2*k)) for k >= 2 and any prime p.
The sequence b(n) := [x^n] ( F(x)/F(-x) )^n, where F(x) = (x^7 - 1)/(x - 1), may satisfy the stronger congruences b(p) == 2 (mod p^3) for prime p > 7 (checked up to p = 499). (End)
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i=0, 0, add(b(n-j, i-1), j=0..min(n, 6))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..30);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 17 2018
STATUS
approved