A174834 A symmetrical triangular sequence:t(n,m)=(StirlingS1[n, m] + StirlingS1[n, n - m])*Binomial[n, m] - (StirlingS1[n, 0] + StirlingS1[n, n - 0])* Binomial[n, 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

Offset

0,5

Comments

Row sums are:

{1, 2, -2, -4, 38, -158, 152, 5280, -73890, 658742, -3723898,...}.

Links

Table of n, a(n) for n=0..47.

Formula

t(n,m)=(StirlingS1[n, m] + StirlingS1[n, n - m])*Binomial[n, m] - (StirlingS1[n, 0] + StirlingS1[n, n - 0])* Binomial[n, 0] + 1

Example

{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},
{1, -3629250, 46235070, -141858000, 165260130, -135739800, 165260130, -141858000, 46235070, -3629250, 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. A154843

Sequence in context: A010323 A353647 A261790 * A100642 A320438 A255511

Adjacent sequences: A174831 A174832 A174833 * A174835 A174836 A174837

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Mar 30 2010

Status

approved