|
Search: id:A154867
|
|
|
| A154867 |
|
A triangular sequence of polynomial coefficients: p(x,n) = Sum[m^n*x^m/m!, {m, 0, Infinity}]/(x*Exp[x]); q(x,n)= If[n == 0, 1, p(x, n) + x^n*p(1/x, n)]. |
|
+0
1
|
|
| 1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 12, 8, 1, 1, 16, 35, 35, 16, 1, 1, 32, 105, 130, 105, 32, 1, 1, 64, 322, 490, 490, 322, 64, 1, 1, 128, 994, 1967, 2100, 1967, 994, 128, 1, 1, 256, 3061, 8232, 9597, 9597, 8232, 3061, 256, 1, 1, 512, 9375, 34855, 48405, 45654, 48405
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Row sums are:
{1, 2, 4, 10, 30, 104, 406, 1754, 8280, 42294, 231950,...}
|
|
FORMULA
|
p(x,n) = Sum[m^n*x^m/m!, {m, 0, Infinity}]/(x*Exp[x]);
q(x,n)= If[n == 0, 1, p(x, n) + x^n*p(1/x, n)];
t(n,m)=coefficients(q(x,n)).
|
|
EXAMPLE
|
{1},
{1, 1},
{1, 2, 1},
{1, 4, 4, 1},
{1, 8, 12, 8, 1},
{1, 16, 35, 35, 16, 1},
{1, 32, 105, 130, 105, 32, 1},
{1, 64, 322, 490, 490, 322, 64, 1},
{1, 128, 994, 1967, 2100, 1967, 994, 128, 1},
{1, 256, 3061, 8232, 9597, 9597, 8232, 3061, 256, 1},
{1, 512, 9375, 34855, 48405, 45654, 48405, 34855, 9375, 512, 1}
|
|
MATHEMATICA
|
Clear[p]; p[x_, n_] = Sum[m^n*x^m/m!, {m, 0, Infinity}]/(x*Exp[x]);
q[x_, n_] = If[n == 0, 1, p[x, n] + x^n*p[1/x, n]];
Table[FullSimplify[ExpandAll[q[x, n]]], {n, 0, 10}];
Table[CoefficientList[FullSimplify[ExpandAll[q[x, n]]], x], {n, 0, 10}];
Flatten[%]
|
|
CROSSREFS
|
Sequence in context: A137854 A062715 A100631 this_sequence A064298 A099594 A117401
Adjacent sequences: A154864 A154865 A154866 this_sequence A154868 A154869 A154870
|
|
KEYWORD
|
nonn,uned,tabl
|
|
AUTHOR
|
Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 16 2009
|
|
|
Search completed in 0.002 seconds
|
