|
Search: id:A154985
|
|
|
| A154985 |
|
Polynomial recursion:m=1; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2)+If[n >= 3, 2^(n - 2)*x*p(x, n - 2), 0]. |
|
+0
1
|
|
| 1, 1, 1, 1, 6, 1, 1, 17, 17, 1, 1, 38, 154, 38, 1, 1, 79, 872, 872, 79, 1, 1, 160, 3991, 14064, 3991, 160, 1, 1, 321, 16791, 157575, 157575, 16791, 321, 1, 1, 642, 68312, 1451486, 4815630, 1451486, 68312, 642, 1, 1, 1283, 274394, 12266038, 107115116, 107115116
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Row sums are:
{1, 2, 8, 36, 232, 1904, 22368, 349376, 7856512, 239313664, 10534962688,...}.
|
|
FORMULA
|
m=1; p(x,n)=(x + 1)*p(x, n - 1) + 2^(m + n - 1)*x*p(x, n - 2)
+If[n >= 3, 2^(n - 2)*x*p(x, n - 2), 0];
t(n,m)=coefficients(p(x,n))
|
|
EXAMPLE
|
{1},
{1, 1},
{1, 6, 1},
{1, 17, 17, 1},
{1, 38, 154, 38, 1},
{1, 79, 872, 872, 79, 1},
{1, 160, 3991, 14064, 3991, 160, 1},
{1, 321, 16791, 157575, 157575, 16791, 321, 1},
{1, 642, 68312, 1451486, 4815630, 1451486, 68312, 642, 1},
{1, 1283, 274394, 12266038, 107115116, 107115116, 12266038, 274394, 1283, 1},
{1, 2564, 1097437, 99979792, 1977283234, 6378236632, 1977283234, 99979792, 1097437, 2564, 1}
|
|
MATHEMATICA
|
Clear[p, n, m, x]; m = 1; p[x, 0] = 1; p[x, 1] = x + 1;
p[x, n] = (x + 1)*p[ x, n - 1] + 2^(m + n - 1)*x*p[x, n - 2]
+ If[n >= 3, 2^(n - 2)*x*p[x, n - 2], 0];
Table[ExpandAll[p[x, n]], {n, 0, 10}];
Table[CoefficientList[ExpandAll[p[x, n]], x], {n, 0, 10}];
Flatten[%]
|
|
CROSSREFS
|
Sequence in context: A152602 A119726 A103999 this_sequence A157275 A157268 A146959
Adjacent sequences: A154982 A154983 A154984 this_sequence A154986 A154987 A154988
|
|
KEYWORD
|
nonn,tabl,uned
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 18 2009
|
|
|
Search completed in 0.002 seconds
|
