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 1-3 of 3 results.

A224097 Numerators of poly-Cauchy numbers c_n^(3).

Original entry on oeis.org

1, 1, -19, 89, -46261, 23323, -114895757, 760567603, -174446569403, 302339104957, -2125170096355349, 3788248001789087, -1573899862241140688567, 317684785943639774839, -2242333884754953400123
Offset: 0

Views

Author

Takao Komatsu, Mar 31 2013

Keywords

Comments

The poly-Cauchy numbers c_n^(k) can be expressed in terms of the (unsigned) Stirling numbers of the first kind: c_n^(k) = (-1)^n*sum(abs(stirling1(n,m))*(-1)^m/(m+1)^k, m=0..n).

Crossrefs

Cf. A006232, A222636, A224095, A224096 (denominators).

Programs

  • Mathematica
    Table[Numerator[Sum[StirlingS1[n, k]/ (k + 1)^3, {k, 0, n}]], {n, 0, 25}]
  • PARI
    a(n) = numerator(sum(k=0, n,stirling(n, k, 1)/(k+1)^3)); \\ Michel Marcus, Nov 15 2015

A224098 Denominators of poly-Cauchy numbers c_n^(4).

Original entry on oeis.org

1, 16, 1296, 6912, 6480000, 2592000, 6223392000, 14224896000, 1440270720000, 320060160000, 2811600481536000, 511200087552000, 255506749760021760000, 291175783202304000, 16846598885276160000
Offset: 0

Views

Author

Takao Komatsu, Mar 31 2013

Keywords

Comments

The poly-Cauchy numbers c_n^(k) can be expressed in terms of the (unsigned) Stirling numbers of the first kind: c_n^(k) = (-1)^n*sum(abs(stirling1(n,m))*(-1)^m/(m+1)^k, m=0..n).

Crossrefs

Cf. A006233, A222748, A224094, A224096, A224099 (numerators).

Programs

  • Mathematica
    Table[Denominator[Sum[StirlingS1[n, k]/ (k + 1)^4, {k, 0, n}]], {n, 0, 25}]
  • PARI
    a(n) = denominator(sum(k=0, n,stirling(n, k, 1)/(k+1)^4)); \\ Michel Marcus, Nov 15 2015

A224100 Denominators of poly-Cauchy numbers c_n^(5).

Original entry on oeis.org

1, 32, 7776, 82944, 388800000, 51840000, 2613824640000, 11948912640000, 3629482214400000, 806551603200000, 77937565348177920000, 14170466426941440000, 92074412343521441433600000
Offset: 0

Views

Author

Takao Komatsu, Mar 31 2013

Keywords

Comments

The poly-Cauchy numbers c_n^(k) can be expressed in terms of the (unsigned) Stirling numbers of the first kind: c_n^(k) = (-1)^n*sum(abs(stirling1(n,m))*(-1)^m/(m+1)^k, m=0..n).

Crossrefs

Cf. A006233, A223023, A224094, A224096, A224098, A224101 (numerators).

Programs

  • Mathematica
    Table[Denominator[Sum[StirlingS1[n, k]/ (k + 1)^5, {k, 0, n}]], {n, 0, 25}]
  • PARI
    a(n) = denominator(sum(k=0, n, stirling(n, k, 1)/(k+1)^5)); \\ Michel Marcus, Nov 15 2015
Showing 1-3 of 3 results.