|
Search: id:A157638
|
|
|
| A157638 |
|
A q-combination triangle sequence :m=1; t(n,k)=If[m == 0, n!, Product[Sum[k*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])]. |
|
+0
1
|
|
| 1, 1, 1, 1, 6, 1, 1, 21, 21, 1, 1, 60, 210, 60, 1, 1, 155, 1550, 1550, 155, 1, 1, 378, 9765, 27900, 9765, 378, 1, 1, 889, 56007, 413385, 413385, 56007, 889, 1, 1, 2040, 302260, 5440680, 14055090, 5440680, 302260, 2040, 1, 1, 4599, 1563660, 66194940
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Row sums are:
{1, 2, 8, 44, 332, 3412, 48188, 940564, 25545052, 969582644, 51635485244,...}.
|
|
FORMULA
|
m=1; t(n,k)=If[m == 0, n!, Product[Sum[k*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].
|
|
EXAMPLE
|
{1},
{1, 1},
{1, 6, 1},
{1, 21, 21, 1},
{1, 60, 210, 60, 1},
{1, 155, 1550, 1550, 155, 1},
{1, 378, 9765, 27900, 9765, 378, 1},
{1, 889, 56007, 413385, 413385, 56007, 889, 1},
{1, 2040, 302260, 5440680, 14055090, 5440680, 302260, 2040, 1},
{1, 4599, 1563660, 66194940, 417028122, 417028122, 66194940, 1563660, 4599, 1},
{1, 10230, 7841295, 761725800, 11286237270, 27523856052, 11286237270, 761725800, 7841295, 10230, 1}
|
|
MATHEMATICA
|
t[n_, m_] = If[m == 0, n!, Product[Sum[k*(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]];
b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])];
Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}]
|
|
CROSSREFS
|
Sequence in context: A060972 A144066 A056941 this_sequence A142596 A155467 A152936
Adjacent sequences: A157635 A157636 A157637 this_sequence A157639 A157640 A157641
|
|
KEYWORD
|
nonn,tabl,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 03 2009
|
|
|
Search completed in 0.002 seconds
|
