|
| |
|
|
A141724
|
|
A triangle of coefficients of a double sum skew 4th level multinomial : t(n,m,k,l)=Sum[Sum[Multinomial[n - m - k - l, m, k, l], {l, 0, k}], {k, 0, m}].
|
|
0
| |
|
|
1, 1, 1, 1, 4, 1, 1, 15, 6, 1, 1, 40, 36, 8, 1, 1, 85, 160, 60, 10, 1, 1, 156, 615, 340, 90, 12, 1, 1, 259, 2016, 1715, 595, 126, 14, 1, 1, 400, 5656, 7616, 3500, 952, 168, 16, 1, 1, 585, 13896, 30408, 18396, 6300, 1428, 216, 18, 1, 1, 820, 30645, 109320, 88620, 37044
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,5
|
|
|
COMMENTS
| Row sums are:
{1, 2, 6, 23, 86, 317, 1215, 4727, 18310, 71249, 279281}.
|
|
|
FORMULA
| t(n,m,k,l)=Sum[Sum[Multinomial[n - m - k - l, m, k, l], {l, 0, k}], {k, 0, m}].
|
|
|
EXAMPLE
| {1},
{1, 1},
{1, 4, 1},
{1, 15, 6, 1},
{1, 40, 36, 8, 1},
{1, 85, 160, 60, 10, 1},
{1, 156, 615, 340, 90, 12, 1},
{1, 259, 2016, 1715, 595, 126, 14, 1},
{1, 400, 5656, 7616, 3500, 952, 168, 16, 1},
{1, 585, 13896, 30408, 18396, 6300, 1428, 216, 18, 1},
{1, 820, 30645, 109320, 88620, 37044, 10500, 2040, 270, 20, 1},
{1, 1111, 61930, 352605, 393030, 200508, 67914, 16500, 2805, 330, 22, 1}
|
|
|
MATHEMATICA
| t[n_, m_, k_, l_] = Multinomial[n - m - k - l, m, k, l]; Table[Table[Sum[Sum[t[n, m, k, l], {l, 0, k}], {k, 0, m}], {m, 0, n}], {n, 0, 11}]; Flatten[%]
|
|
|
CROSSREFS
| Cf A065109.
Sequence in context: A202906 A177984 A157013 * A157211 A176428 A116469
Adjacent sequences: A141721 A141722 A141723 * A141725 A141726 A141727
|
|
|
KEYWORD
| nonn,uned
|
|
|
AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 12 2008
|
| |
|
|
