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A281267
Main diagonal of A276554.
6
1, -1, -3, 8, 13, -51, -120, 538, 781, -5419, -3053, 47673, 5080, -427740, 136462, 3922383, -3278067, -34819588, 48561567, 299316651, -603368637, -2509708844, 6948730643, 20210062532, -76150197416, -152569240051, 801154765564, 1039352472008, -8158396721266
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
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