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%I #23 Apr 20 2023 11:51:03
%S 1,-1,-3,8,13,-51,-120,538,781,-5419,-3053,47673,5080,-427740,136462,
%T 3922383,-3278067,-34819588,48561567,299316651,-603368637,-2509708844,
%U 6948730643,20210062532,-76150197416,-152569240051,801154765564,1039352472008,-8158396721266
%N Main diagonal of A276554.
%C From _Peter Bala_, Apr 18 2023: (Start)
%C 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.
%C 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)
%H Seiichi Manyama, <a href="/A281267/b281267.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = [x^n] exp(-n*Sum_{k>=1} x^k/(k*(1 - x^k)^2)). - _Ilya Gutkovskiy_, May 30 2018
%t nmax = 40; Table[SeriesCoefficient[Product[(1 - x^k)^(n*k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}] (* _Vaclav Kotesovec_, Apr 17 2017 *)
%Y Cf. A255672, A270922, A276554.
%K sign
%O 0,3
%A _Seiichi Manyama_, Apr 13 2017