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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A283163 Expansion of exp( Sum_{n>=1} -sigma(4*n)*x^n/n ) in powers of x.

Original entry on oeis.org

1, -7, 17, -14, 2, -21, 36, 13, -26, -24, 10, 12, -17, 34, 22, 19, -96, -10, 14, 38, 0, 12, -23, 72, -38, -2, -11, -64, -34, 0, 72, 84, -26, 0, 0, -79, 60, 24, -32, -58, -7, -84, 50, 26, 120, 0, 0, 46, -34, -64, 10, -119, 70, 0, 22, -70, 36, 37, -120, 0
Offset: 0

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Author

Seiichi Manyama, Mar 02 2017

Keywords

Crossrefs

Cf. A182820 (exp( Sum_{n>=1} sigma(4*n)*x^n/n )), A193553 (sigma(4*n)).
Cf. exp( Sum_{n>=1} -sigma(k*n)*x^n/n ): A115110 (k=2), A185654 (k=3), this sequence (k=4), A282937 (k=5), A283164 (k=6), A282942 (k=7), A283168 (k=8), A283169 (k=9).

Formula

G.f.: Product_{n>=1} (1 - x^n)^7/(1 - x^(2*n))^3.
a(n) = -(1/n)*Sum_{k=1..n} sigma(4*k)*a(n-k). - Seiichi Manyama, Mar 04 2017

A319362 a(n) = [x^n] exp(Sum_{k>=1} sigma(n*k)*x^k/k).

Original entry on oeis.org

1, 1, 8, 39, 385, 917, 31247, 22527, 1081986, 2464860, 50099635, 14931071, 19684696065, 394805109, 82267017929, 496514888157, 11386442827781, 284625019799, 3469798073972537, 7725084195239, 136470024990370842, 28400489198168457, 241211623942678951, 5776331152550399
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 17 2018

Keywords

Crossrefs

Programs

  • Mathematica
    Table[SeriesCoefficient[Exp[Sum[DivisorSigma[1, n k] x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 23}]
Previous Showing 11-12 of 12 results.