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%I #10 Apr 20 2023 11:51:10
%S 1,2,16,128,1056,8952,77200,673948,5937792,52689170,470210016,
%T 4215834328,37945215552,342650763392,3102866408560,28166168335128,
%U 256220106742272,2335126111557564,21317113277158336,194890649121580880,1784158030393621056,16353089279998330456
%N Coefficient of x^n in Product_{k>=1} ((1 + x^k) / (1 - x^k))^(k*n).
%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 Vaclav Kotesovec, <a href="/A270924/b270924.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) ~ c * d^n / sqrt(n), where d = 9.38812912875337022533876219516002188057967... and c = 0.2845468763296311652189248055322905919858...
%t Table[SeriesCoefficient[Product[((1+x^k)/(1-x^k))^(k*n), {k, 1, n}], {x, 0, n}], {n, 0, 25}]
%Y Cf. A255672, A270922, A270919, A270923.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Mar 26 2016