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A343351
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Expansion of Product_{k>=1} 1 / (1 - x^k)^(6^(k-1)).
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7
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1, 1, 7, 43, 280, 1792, 11586, 74550, 479892, 3083640, 19794678, 126908502, 812761299, 5199586119, 33230586285, 212172173565, 1353444677529, 8626044781761, 54931168743703, 349524243121795, 2222294161109422, 14119034725444774, 89639674321304392, 568720801952770012
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ exp(sqrt(2*n/3) - 1/12 + c/6) * 6^(n - 1/4) / (2*sqrt(Pi)*n^(3/4)), where c = Sum_{j>=2} 1/(j * (6^(j-1) - 1)). - Vaclav Kotesovec, Apr 12 2021
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MAPLE
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a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(
d*6^(d-1), d=numtheory[divisors](j)), j=1..n)/n)
end:
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MATHEMATICA
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nmax = 23; CoefficientList[Series[Product[1/(1 - x^k)^(6^(k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, (1/n) Sum[Sum[d 6^(d - 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 23}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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