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A341876
E.g.f.: Product_{i>=1, j>=1} (1 + x^(i*j)/(i*j)!) / (1 - x^(i*j)/(i*j)!).
3
1, 2, 8, 40, 230, 1584, 12096, 103828, 975284, 10045182, 111724064, 1342990356, 17288290776, 238095398064, 3488772309480, 54304690352816, 894465560384026, 15564259644205288, 285282543243628356, 5498843253154821196, 111203939051325462504, 2355689449259544720344
OFFSET
0,2
COMMENTS
Exponential convolution of A341505 and A341506.
LINKS
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...
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]!
CROSSREFS
Sequence in context: A343146 A209358 A116456 * A305406 A296050 A347666
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 22 2021
STATUS
approved