A341876 - OEIS

%I #6 Feb 22 2021 07:32:28

%S 1,2,8,40,230,1584,12096,103828,975284,10045182,111724064,1342990356,

%T 17288290776,238095398064,3488772309480,54304690352816,

%U 894465560384026,15564259644205288,285282543243628356,5498843253154821196,111203939051325462504,2355689449259544720344

%N E.g.f.: Product_{i>=1, j>=1} (1 + x^(i*j)/(i*j)!) / (1 - x^(i*j)/(i*j)!).

%C Exponential convolution of A341505 and A341506.

%H Vaclav Kotesovec, <a href="/A341876/b341876.txt">Table of n, a(n) for n = 0..447</a>

%F a(n) = Sum_{k=0..n} binomial(n,k) * A341505(k) * A341506(n-k).

%F a(n) ~ c * n!, where c = 2*Product_{k>=2} ((k!+1)/(k!-1))^sigma_0(k) = 47.4139841600096613008093034069984807541890052309118213077603602425211186...

%t nmax = 25; CoefficientList[Series[Product[(1 + x^(i*j)/(i*j)!)/(1 - x^(i*j)/(i*j)!), {i, 1, nmax}, {j, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!

%t nmax = 25; CoefficientList[Series[Product[((1 + x^k/k!)/(1 - x^k/k!))^DivisorSigma[0, k], {k, 1, nmax}], {x, 0, nmax}], x]*Range[0, nmax]!

%Y Cf. A341505, A341506.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Feb 22 2021