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.

Showing 1-2 of 2 results.

A305209 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - n*x^k))).

Original entry on oeis.org

1, 1, 2, 12, 86, 885, 11234, 172711, 3112262, 64422126, 1506406702, 39279802969, 1130133725736, 35566642690293, 1215444767739120, 44823725114186355, 1774344335649148230, 75042087586212893216, 3377041177800135323864, 161125608740713509132809, 8124438293071792011560256
Offset: 0

Views

Author

Ilya Gutkovskiy, May 27 2018

Keywords

Crossrefs

Programs

  • Mathematica
    Table[SeriesCoefficient[Exp[Sum[(-1)^(k + 1) x^k/(k (1 - n x^k)), {k, 1, n}]], {x, 0, n}], {n, 0, 20}]
    Table[SeriesCoefficient[Product[(1 + x^k)^(n^(k - 1)), {k, 1, n}], {x, 0, n}], {n, 0, 20}]

Formula

a(n) = [x^n] Product_{k>=1} (1 + x^k)^(n^(k-1)).

A319361 a(n) = [x^n] exp(Sum_{k>=1} sigma_n(k)*x^k/k).

Original entry on oeis.org

1, 1, 3, 14, 136, 2411, 88903, 6309849, 866470849, 240522266760, 132000248840652, 141226630324344532, 306101744973083495408, 1327520858367342045830198, 11328405846086223895036194126, 196814026990537767059856457640779, 6894163531963490274906095710739747873
Offset: 0

Views

Author

Ilya Gutkovskiy, Sep 17 2018

Keywords

Crossrefs

Diagonal of A144048.

Programs

  • Mathematica
    Table[SeriesCoefficient[Exp[Sum[DivisorSigma[n, k] x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 16}]
    Table[SeriesCoefficient[Product[1/(1 - x^k)^(k^(n - 1)), {k, 1, n}], {x, 0, n}], {n, 0, 16}]

Formula

a(n) = [x^n] Product_{k>=1} 1/(1 - x^k)^(k^(n-1)).
Showing 1-2 of 2 results.