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A270924
Coefficient of x^n in Product_{k>=1} ((1 + x^k) / (1 - x^k))^(k*n).
7
1, 2, 16, 128, 1056, 8952, 77200, 673948, 5937792, 52689170, 470210016, 4215834328, 37945215552, 342650763392, 3102866408560, 28166168335128, 256220106742272, 2335126111557564, 21317113277158336, 194890649121580880, 1784158030393621056, 16353089279998330456
OFFSET
0,2
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) ~ c * d^n / sqrt(n), where d = 9.38812912875337022533876219516002188057967... and c = 0.2845468763296311652189248055322905919858...
MATHEMATICA
Table[SeriesCoefficient[Product[((1+x^k)/(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