A174555 Triangle read by rows: T(n,m) = S(n,m) + S(n,n-m) where S(n,m) = Sum_{k=0..n} Stirling2(n, k) * Stirling1(n - k, m) * binomial(n, k) * (-1)^(m - k).

2, -1, -1, 1, 4, 1, -1, -15, -15, -1, 1, 78, 108, 78, 1, -1, -635, -935, -935, -635, -1, 1, 7605, 12315, 9600, 12315, 7605, 1, -1, -123396, -225071, -147700, -147700, -225071, -123396, -1, 1, 2570484, 5190598, 3588508, 1936340, 3588508, 5190598

Offset

0,1

Links

Table of n, a(n) for n=0..42.

Example

Triangle begins:
  {2},
  {-1, -1},
  {1, 4, 1},
  {-1, -15, -15, -1},
  {1, 78, 108, 78, 1},
  {-1, -635, -935, -935, -635, -1},
  {1, 7605, 12315, 9600, 12315, 7605, 1}, ...

Mathematica

t[n_, m_] = Sum[StirlingS2[n, k]*StirlingS1[n - k, m]*Binomial[ n, k]*(-1)^(m - k), {k, 0, n}];
Table[Table[t[n, m] + t[n, n - m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A157114 A156786 A156141 * A157113 A214712 A213330

Adjacent sequences: A174552 A174553 A174554 * A174556 A174557 A174558

Keyword

sign,tabl

Author

Roger L. Bagula, Mar 22 2010

Extensions

Edited by Sean A. Irvine, Feb 28 2026

Status

approved