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A338676
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Expansion of Product_{k>=1} 1 / (1 - 7^(k-1)*x^k).
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9
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1, 1, 8, 57, 449, 3193, 25145, 178809, 1391314, 9996498, 76955586, 552257546, 4255024523, 30502987019, 232969386483, 1682476714724, 12762937304013, 92019035596293, 698222541789109, 5030814634614406, 37955614705675479, 274741644961416648, 2061916926761604144, 14909943849253537057
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..23.
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FORMULA
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a(n) = Sum_{k=0..n} p(n,k) * 7^(n-k), where p(n,k) = number of partitions of n into k parts.
a(n) ~ sqrt(6) * polylog(2, 1/7)^(1/4) * 7^(n - 1/2) * exp(2*sqrt(polylog(2, 1/7)*n)) / (2*sqrt(Pi)*n^(3/4)). - Vaclav Kotesovec, May 09 2021
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MATHEMATICA
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nmax = 23; CoefficientList[Series[Product[1/(1 - 7^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Table[Sum[Length[IntegerPartitions[n, {k}]] 7^(n - k), {k, 0, n}], {n, 0, 23}]
a[n_] := a[n] = If[n == 0, 1, (1/n) Sum[Sum[d 7^(k - k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 23}]
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CROSSREFS
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Cf. A008284, A075900, A246939, A300579, A338673, A338674, A338675, A338677, A338678, A338679.
Sequence in context: A281912 A343352 A307642 * A199555 A241594 A241595
Adjacent sequences: A338673 A338674 A338675 * A338677 A338678 A338679
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Apr 23 2021
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STATUS
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approved
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