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 1-4 of 4 results.

A224102 Numerators of poly-Cauchy numbers of the second kind hat c_n^(2).

Original entry on oeis.org

1, -1, 13, -43, 5647, -3401, 2763977, -10326059, 876576493, -1665984623, 1156096889861, -2220482068331, 75970695882225719, -1088498788093641, 855021689397409453, -3324381371618385007, 4010325276269988793421
Offset: 0

Views

Author

Takao Komatsu, Mar 31 2013

Keywords

Comments

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

Crossrefs

Cf. A002657, A223899, A219247 (denominators).

Programs

  • Mathematica
    Table[Numerator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^2, {k, 0, n}]], {n, 0,
      25}]
  • PARI
    a(n) = numerator(sum(k=0, n, stirling(n, k, 1)*(-1)^k/(k+1)^2)); \\ Michel Marcus, Nov 14 2015

A224103 Denominators of poly-Cauchy numbers of the second kind hat c_n^(3).

Original entry on oeis.org

1, 8, 216, 576, 108000, 43200, 14817600, 16934400, 571536000, 127008000, 101428588800, 18441561600, 709031939616000, 1731457728000, 373994869248, 24932991283200, 229679599076928000, 491293260057600
Offset: 0

Views

Author

Takao Komatsu, Mar 31 2013

Keywords

Comments

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

Crossrefs

Cf. A002790, A223901, A219247, A224104 (numerators).

Programs

  • Mathematica
    Table[Denominator[Sum[StirlingS1[n, k] (-1)^k/ (k + 1)^3, {k, 0, n}]], {n, 0, 25}]
  • PARI
    a(n) = denominator(sum(k=0, n, stirling(n, k, 1)*(-1)^k/(k+1)^3)); \\ Michel Marcus, Nov 14 2015

A224105 Denominators of poly-Cauchy numbers of the second kind hat c_n^(4).

Original entry on oeis.org

1, 16, 1296, 6912, 6480000, 288000, 6223392000, 14224896000, 1440270720000, 64012032000, 562320096307200, 511200087552000, 255506749760021760000, 1455878916011520000, 673863955411046400, 17969705477627904000
Offset: 0

Views

Author

Takao Komatsu, Mar 31 2013

Keywords

Comments

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

Crossrefs

Cf. A002790, A223902, A219247, A224103, A224106 (numerators).

Programs

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

A224107 Denominators of poly-Cauchy numbers of the second kind hat c_n^(5).

Original entry on oeis.org

1, 32, 7776, 82944, 388800000, 155520000, 2613824640000, 11948912640000, 3629482214400000, 806551603200000, 77937565348177920000, 14170466426941440000, 92074412343521441433600000, 524640526173911347200000, 6070840374298117017600000, 12951126131835982970880000
Offset: 0

Views

Author

Takao Komatsu, Mar 31 2013

Keywords

Comments

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

Crossrefs

Cf. A002790, A223904, A219247, A224103, A224105, A224109 (numerators).

Programs

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

Extensions

More terms from Michel Marcus, Nov 15 2015
Showing 1-4 of 4 results.