OFFSET
0,3
COMMENTS
From Peter Bala, Apr 18 2023: (Start)
The Gauss congruences a(n*p^k) == a(n*p^(k-1)) (mod p^k) hold for all primes p and all positive integers n and k.
Conjecture: the stronger supercongruences a(n*p^k) == a(n*p^(k-1)) (mod p^(2*k)) hold for all primes p >= 3 and all positive integers n and k. (End)
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..100
FORMULA
a(n) = [x^n] exp(-n*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, May 30 2018
MATHEMATICA
nmax = 40; Table[SeriesCoefficient[Product[(1 - x^k)^(n*k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}] (* Vaclav Kotesovec, Apr 17 2017 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 13 2017
STATUS
approved