|
Search: id:A154231
|
|
|
| A154231 |
|
A recursive triangular sequence: A(n,k)= A(n - 1, k - 1) + A(n - 1, k) +(n^2*(n + 1)^2*(2*n^2 + 2*n - 1)/12)*A(n - 2, k - 1). |
|
+0
1
|
|
| 1, 1, 1, 1, 278, 1, 1, 1579, 1579, 1, 1, 6005, 1233308, 6005, 1, 1, 18207, 20504692, 20504692, 18207, 1, 1, 47216, 194715939, 35816807848, 194715939, 47216, 1, 1, 108993, 1319518787, 1302709376779, 1302709376779, 1319518787, 108993, 1, 1
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Row sums are:
{1, 2, 280, 3160, 1245320, 41045800, 36206334160, 2608058009120,
4379846440900240, 584684102745724480,...}.
|
|
FORMULA
|
A(n,k)= A(n - 1, k - 1) + A(n - 1, k) +(n^2*(n + 1)^2*(2*n^2 + 2*n - 1)/12)*A(n - 2, k - 1).
|
|
EXAMPLE
|
{1},
{1, 1},
{1, 278, 1},
{1, 1579, 1579, 1},
{1, 6005, 1233308, 6005, 1},
{1, 18207, 20504692, 20504692, 18207, 1},
{1, 47216, 194715939, 35816807848, 194715939, 47216, 1},
{1, 108993, 1319518787, 1302709376779, 1302709376779, 1319518787, 108993, 1},
{1, 229819, 7024500980, 24830582225241, 4330171226988158, 24830582225241, 7024500980, 229819, 1},
{1, 450645, 31093110024, 316220342865496, 292025799936436074, 292025799936436074, 316220342865496, 31093110024, 450645, 1}
|
|
MATHEMATICA
|
A[n_, 1] := 1; A[n_, n_] := 1;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (n^2*(n + 1)^2*(2*n^2 + 2*n - 1)/12)*A[n - 2, k - 1];
Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]
|
|
CROSSREFS
|
Sequence in context: A142831 A105977 A048525 this_sequence A056995 A062384 A053345
Adjacent sequences: A154228 A154229 A154230 this_sequence A154232 A154233 A154234
|
|
KEYWORD
|
nonn,uned,tabl
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 05 2009
|
|
|
Search completed in 0.002 seconds
|
