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.

A219247 Denominators of poly-Cauchy numbers of the second kind hat c_n^(2).

Original entry on oeis.org

1, 4, 36, 48, 1800, 240, 35280, 20160, 226800, 50400, 3659040, 665280, 1967565600, 2242240, 129729600, 34594560, 2677989600, 66830400, 1857684628800, 39109150080, 3226504881600, 307286179200, 2333316585600, 1285014931200, 2192556726360000, 25057791158400
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, A223899, A224102 (numerators).

Programs

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

A224104 Numerators of poly-Cauchy numbers of the second kind hat c_n^(3).

Original entry on oeis.org

1, -1, 35, -217, 135989, -236881, 435876493, -3174551347, 790667708347, -1473406853309, 11050163107919893, -20886680047664287, 9154917271574968829623, -277315386220087376401, 803143323197313772705
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, A223901, A224102, A224103 (denominators).

Programs

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

A224109 Numerators of poly-Cauchy numbers of the second kind hat c_n^(5).

Original entry on oeis.org

1, -1, 275, -6289, 92902541, -154473289, 13399738273333, -377635608584803, 822223497000264427, -1492945924219675973, 1323386773861946436609781, -2448418399924413951578983, 177825546947844845937070681472647
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

Programs

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