|
| |
|
|
A176153
|
|
Triangle read by rows:t(n,m)=Sum[StirlingS1[n, n - k]*Binomial[n, k], {k, 0, m}]
|
|
0
|
|
|
|
1, 1, 1, 1, -1, -1, 1, -8, -2, -2, 1, -23, 43, 19, 19, 1, -49, 301, -199, -79, -79, 1, -89, 1186, -3314, 796, 76, 76, 1, -146, 3529, -22196, 34644, -2400, 2640, 2640, 1, -223, 8793, -100967, 372863, -362529, 3375, -36945, -36945, 1, -323, 19333, -361691
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,8
|
|
|
COMMENTS
|
Row sums are:
{2, -1, -11, 59, -104, -1268, 18712, -152577, 650050, 5365931,...}.
|
|
|
LINKS
|
Table of n, a(n) for n=0..48.
|
|
|
FORMULA
|
t(n,m)=Sum[StirlingS1[n, n - k]*Binomial[n, k], {k, 0, m}]
|
|
|
EXAMPLE
|
{1},
{1, 1},
{1, -1, -1},
{1, -8, -2, -2},
{1, -23, 43, 19, 19},
{1, -49, 301, -199, -79, -79},
{1, -89, 1186, -3314, 796, 76, 76},
{1, -146, 3529, -22196, 34644, -2400, 2640, 2640},
{1, -223, 8793, -100967, 372863, -362529, 3375, -36945, -36945},
{1, -323, 19333, -361691, 2466883, -6010901, 3911515, -33509, 329371, 329371},
{1, -449, 38701, -1095299, 12192031, -55677869, 96294931, -44429069, 1766851, -1861949, -1861949}
|
|
|
MATHEMATICA
|
t[n_, m_] := Sum[StirlingS1[n, n - k]*Binomial[n, k], {k, 0, m}];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
|
|
|
CROSSREFS
|
Sequence in context: A177428 A130617 A010150 * A136711 A037920 A138997
Adjacent sequences: A176150 A176151 A176152 * A176154 A176155 A176156
|
|
|
KEYWORD
|
sign,tabl,uned
|
|
|
AUTHOR
|
Roger L. Bagula, Apr 10 2010
|
|
|
STATUS
|
approved
|
| |
|
|
