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.

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

A224106 Numerators of poly-Cauchy numbers of the second kind hat c_n^(4).

Original entry on oeis.org

1, -1, 97, -1147, 3472243, -653983, 74118189437, -1058923294571, 777910456216513, -285577840060819, 23240203016832136201, -216925341603548096639, 1222007019804929270080450811
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, A223902, A224105, A114102, A224104, A224105 (denominators).

Programs

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