A341876 E.g.f.: Product_{i>=1, j>=1} (1 + x^(i*j)/(i*j)!) / (1 - x^(i*j)/(i*j)!).

1, 2, 8, 40, 230, 1584, 12096, 103828, 975284, 10045182, 111724064, 1342990356, 17288290776, 238095398064, 3488772309480, 54304690352816, 894465560384026, 15564259644205288, 285282543243628356, 5498843253154821196, 111203939051325462504, 2355689449259544720344

Offset: 0

Author

Vaclav Kotesovec, Feb 22 2021

Keywords

• nonn

Comments

Exponential convolution of A341505 and A341506.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..447

Crossrefs

Cf. A341505, A341506.

Programs

Mathematica

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]!
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]!

Formula

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

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