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.

Previous Showing 31-32 of 32 results.

A356342 a(n) = Sum_{k=1..n} binomial(2*n, k) * sigma_2(k).

Original entry on oeis.org

2, 34, 281, 2178, 12397, 79729, 398932, 2224354, 10959221, 56341309, 255685080, 1334248401, 5892916876, 28082515768, 127714609741, 604178948098, 2590365128017, 12284868071365, 52160408294826, 241445420212893, 1049251819301974, 4674022621994716, 19563451165603647
Offset: 1

Views

Author

Vaclav Kotesovec, Aug 04 2022

Keywords

Crossrefs

Cf. A001157, A064602, A351146, A356038.

Programs

  • Mathematica
    Table[Sum[Binomial[2*n, k]*DivisorSigma[2, k], {k, 1, n}], {n, 1, 30}]
  • PARI
    a(n) = sum(k=1, n, binomial(2*n, k) * sigma(k, 2)); \\ Michel Marcus, Aug 05 2022

Formula

a(n) ~ zeta(3) * n^2 * 2^(2*n-1).

A356345 a(n) = Sum_{k=1..n} binomial(2*k, k) * sigma_2(k).

Original entry on oeis.org

2, 32, 232, 1702, 8254, 54454, 226054, 1320004, 5744424, 29762704, 115825408, 683698168, 2451800168, 12480950168, 52811505368, 257779918358, 934525722158, 5063712283658, 17858697779258, 93122902514978, 362251839734978, 1645752207604178, 6009470493232178, 33419933623867178
Offset: 1

Views

Author

Vaclav Kotesovec, Aug 04 2022

Keywords

Comments

The average value of a(n) is zeta(3) * n^(3/2) * 4^(n+1) / (3*sqrt(Pi)).

Crossrefs

Cf. A001157, A064602, A351146, A356038.

Programs

  • Mathematica
    Table[Sum[Binomial[2*k, k]*DivisorSigma[2, k], {k, 1, n}], {n, 1, 30}]
  • PARI
    a(n) = sum(k=1, n, binomial(2*k, k) * sigma(k, 2)); \\ Michel Marcus, Aug 05 2022
Previous Showing 31-32 of 32 results.

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