OFFSET
0,3
COMMENTS
FORMULA
Conjectures:
1) a(p) == 2*p - 1 (mod p^4) for all primes p >= 5 (checked up to p = 101).
More generally, the supercongruence a(p^k) == 2*p^k - 1 (mod p^(3+k)) may hold for all primes p >= 5 and all k >= 1.
2) a(p-1) == 1 (mod p^3) for all primes p except p = 3 (checked up to p = 101).
More generally, the supercongruence a(p^k - p^(k-1)) == 1 (mod p^(2+k)) may hold for all primes p >= 5 and all k >= 1.
MAPLE
a(n) := coeff(series( 1/(1 + x) * LegendreP(n, (1 - x)/(1 + x))^(-n), x, 21), x, n):
seq(a(n), n = 0..20);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Bala, Jul 18 2023
STATUS
approved