A321042 - OEIS

%I #9 Oct 28 2018 03:49:08

%S 1,1,5,37,491,12763,690756,70250881,13805853214,5567873958982,

%T 4386114219458332,6711687353310594027,21048327399504558833175,

%U 131214860796100022696745520,1603892616451767287785208156624,40296605442098101265893075903063822,2031406440758379976992019043333960734724

%N a(n) = [x^n] Product_{k>=1} (1 + x^k)^sigma_n(k).

%H Seiichi Manyama, <a href="/A321042/b321042.txt">Table of n, a(n) for n = 0..80</a>

%F a(n) = [x^n] Product_{i>=1, j>=1} (1 + x^(i*j))^(j^n).

%F a(n) = [x^n] exp(Sum_{k>=1} sigma_(n+1)(k)*x^k/(k*(1 - x^(2*k)))).

%t Table[SeriesCoefficient[Product[(1 + x^k)^DivisorSigma[n, k], {k, 1, n}], {x, 0, n}], {n, 0, 16}]

%t Table[SeriesCoefficient[Product[Product[(1 + x^(i j))^(j^n), {j, 1, n}], {i, 1, n}], {x, 0, n}], {n, 0, 16}]

%t Table[SeriesCoefficient[Exp[Sum[DivisorSigma[n + 1, k] x^k/(k (1 - x^(2 k))), {k, 1, n}]], {x, 0, n}], {n, 0, 16}]

%Y Cf. A107742, A192065, A288414, A288415, A301548, A301549, A301550, A301551, A301552, A301553, A319647.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Oct 26 2018