A174834 Triangle read by rows: T(n,k) = (Stirling1(n,k) + Stirling1(n,n-k)) * binomial(n,k) with T(0,0)=1.

1, 1, 1, 1, -4, 1, 1, -3, -3, 1, 1, -48, 132, -48, 1, 1, 70, -150, -150, 70, 1, 1, -810, 5385, -9000, 5385, -810, 1, 1, 4893, -33369, 31115, 31115, -33369, 4893, 1, 1, -40544, 374920, -845152, 947660, -845152, 374920, -40544, 1, 1, 362556, -3925368, 9541392, -5649210, -5649210, 9541392, -3925368, 362556, 1

Offset

0,5

Comments

Triangle is symmetric.

Links

Table of n, a(n) for n=0..54.

Example

Triangle begins:
  {1},
  {1, 1},
  {1, -4, 1},
  {1, -3, -3, 1},
  {1, -48, 132, -48, 1},
  {1, 70, -150, -150, 70, 1},
  {1, -810, 5385, -9000, 5385, -810, 1},
  ...

Mathematica

t[n_, m_]=( StirlingS1[n, m]+StirlingS1[n, n-m])*Binomial[n, m]-(StirlingS1[n, 0]+StirlingS1[n, n-0])*Binomial[n, 0]+1;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A008275, A154843.

Sequence in context: A353647 A261790 A392664 * A100642 A320438 A255511

Adjacent sequences: A174831 A174832 A174833 * A174835 A174836 A174837

Keyword

sign,tabl,less

Author

Roger L. Bagula, Mar 30 2010

Extensions

Edited by Sean A. Irvine, Mar 14 2026

Status

approved