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 1-2 of 2 results.

A211210 a(n) = Sum_{k=0..n} binomial(n, k)*|S1(n, k)|.

Original entry on oeis.org

1, 1, 3, 16, 115, 1021, 10696, 128472, 1734447, 25937683, 424852351, 7554471156, 144767131444, 2971727661124, 65013102375404, 1509186299410896, 37032678328740751, 957376811266995031, 25999194631060525009, 739741591417352081464, 22000132609456951524051
Offset: 0

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Author

Olivier Gérard, Oct 23 2012

Keywords

Comments

Binomial convolution of the unsigned Stirling numbers of the first kind.
Row sums of triangle A187555.

Crossrefs

Cf. A317274 (signed S1), A187555, A134090, A211211.
Cf. A122455 (second kind), A271702, A134094, A343841 (second kind inverse).

Programs

  • Mathematica
    Table[Sum[Binomial[n, k] Abs[StirlingS1[n, k]], {k, 0, n}], {n, 0, 20}]
  • PARI
    a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(n, k, 1))); \\ Michel Marcus, May 10 2021

A344053 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*Stirling2(n, k)*k!.

Original entry on oeis.org

1, 1, 0, -9, -40, 125, 3444, 18571, -241872, -5796711, -24387220, 1132278191, 25132445832, 8850583573, -10681029498972, -214099676807085, 1643397436986464, 176719161389104817, 2976468247699317468, -71662294521163070153, -4638920054290748840520, -55645074852328083377619
Offset: 0

Views

Author

Peter Luschny, May 10 2021

Keywords

Comments

Inverse binomial convolution of the Fubini numbers (A131689).

Crossrefs

Programs

  • Mathematica
    a[n_] := Sum[(-1)^(n - k) * Binomial[n, k] * StirlingS2[n, k] * k!, {k, 0, n}]; Array[a, 22, 0] (* Amiram Eldar, May 10 2021 *)
  • PARI
    a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n, k)*stirling(n, k, 2)*k!); \\ Michel Marcus, May 10 2021

Formula

a(n) = Sum_{k=0..n} (-1)^k * A219859(n,k). - Alois P. Heinz, Jan 24 2022
a(n) = n! * [x^n] (2 - exp(-x))^n. - Fabian Pereyra, Aug 31 2024
Showing 1-2 of 2 results.