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
Vaclav Kotesovec, Table of n, a(n) for n = 0..500
FORMULA
a(n) ~ c * d^n / sqrt(n), where d = 5.86811560195778704624328861800917668... and c = 0.25351514412215050116013727161633502...
a(n) = [x^n] exp(n*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, May 30 2018
MATHEMATICA
Table[SeriesCoefficient[Product[(1+x^k)^(k*n), {k, 1, n}], {x, 0, n}], {n, 0, 25}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 26 2016
STATUS
approved