|
|
A168621
|
|
Triangle read by rows: T(n,0) = T(n,n) = 1 for n >= 0, T(n,k) = ((n - 1)! + 1)*binomial(n, k) for 1 <= k <= n - 1, n >= 2.
|
|
0
|
|
|
1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 28, 42, 28, 1, 1, 125, 250, 250, 125, 1, 1, 726, 1815, 2420, 1815, 726, 1, 1, 5047, 15141, 25235, 25235, 15141, 5047, 1, 1, 40328, 141148, 282296, 352870, 282296, 141148, 40328, 1, 1, 362889, 1451556, 3386964, 5080446, 5080446, 3386964, 1451556, 362889, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
COMMENTS
|
Row 0 is 1, and row n gives the coefficients in the expansion of (x + 1)^n + (n - 1)!*((x + 1)^n - x^n -1). - Franck Maminirina Ramaharo, Dec 22 2018
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: exp((1 + x)*y) + log((1 - y)*(1 - x*y)/(1 - (1 + x)*y)). (End)
|
|
EXAMPLE
|
Triangle begins:
1;
1, 1;
1, 4, 1;
1, 9, 9, 1;
1, 28, 42, 28, 1;
1, 125, 250, 250, 125, 1;
1, 726, 1815, 2420, 1815, 726, 1;
1, 5047, 15141, 25235, 25235, 15141, 5047, 1;
1, 40328, 141148, 282296, 352870, 282296, 141148, 40328, 1;
...
|
|
MATHEMATICA
|
p[x_, n_] := If[n == 0, 1, (x + 1)^n + (n - 1)!*((x + 1)^n - x^n - 1)];
|
|
PROG
|
(Maxima) T(n, k) := if k = 0 or k = n then 1 else ((n - 1)! + 1)*binomial(n, k)$
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|