A174555 Triangle read by rows:s(n,m)=Sum[StirlingS2[n, k]*StirlingS1[n - k, m]* Binomial[n, k]*(-1)^(m - k), {k, 0, n}];t[n,m]=s[n,m]+s[n,n-m]

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

Comments

Row sums are:

{2, -2, 6, -32, 266, -3142, 49442, -992336, 24635522, -738902954, 26271105662,...}.

Links

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

Formula

s(n,m)=Sum[StirlingS2[n, k]*StirlingS1[n - k, m]* Binomial[n, k]*(-1)^(m - k), {k, 0, n}];

t[n,m]=s[n,m]+s[n,n-m]

Example

{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, 2570484, 1},
{-1, -66359889, -145212474, -112391706, -45487407, -45487407, -112391706, -145212474, -66359889, -1},
{1, 2069254630, 4829689875, 4139150270, 1738086315, 718743480, 1738086315, 4139150270, 4829689875, 2069254630, 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,uned

Author

Roger L. Bagula, Mar 22 2010

Status

approved