cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A318025 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1/(1 - j*x^(k*j))).

Original entry on oeis.org

1, 4, 7, 18, 26, 66, 98, 216, 361, 701, 1171, 2287, 3763, 6887, 11707, 20740, 34637, 60678, 100581, 172609, 285924, 481671, 791317, 1323831, 2156856, 3561119, 5784021, 9459559, 15250217, 24783964, 39713789, 64032664, 102200203, 163617694, 259745174, 413886941, 653715969, 1035539948
Offset: 1

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Author

Ilya Gutkovskiy, Aug 23 2018

Keywords

Comments

Inverse Moebius transform of A006906.

Crossrefs

Programs

  • Mathematica
    nmax = 38; Rest[CoefficientList[Series[Sum[-1 + Product[1/(1 - j x^(k j)), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x]]
    b[n_] := b[n] = SeriesCoefficient[Product[1/(1 - k x^k), {k, 1, n}], {x, 0, n}]; a[n_] := a[n] = SeriesCoefficient[Sum[b[k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}]; Table[a[n], {n, 38}]
    Table[Sum[Total[Times @@@ IntegerPartitions[d]], {d, Divisors[n]}], {n, 38}]

Formula

G.f.: Sum_{k>=1} A006906(k)*x^k/(1 - x^k).
a(n) = Sum_{d|n} A006906(d).
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