|
|
A223535
|
|
Coefficients of (x^(1/5)*d/dx)^n for positive integer n.
|
|
0
|
|
|
1, 1, 5, -3, 15, 25, 21, -45, 150, 125, -231, 375, -375, 1250, 625, 693, -981, 750, -375, 1875, 625, -13167, 17199, -11655, 5250, 13125, 3125, 302841, -375417, 237510, -100275, 26250, 26250, 87500, 15625, 8176707, -9773379, 5914755, -2390850, 685125, -78750
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
These are generalized Stirling numbers.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: exp(((1+4/5*x*y)^(5/4)-1)/x).
|
|
EXAMPLE
|
1;
1, 5;
-3, 15, 25;
21, -45, 150, 125;
-231, 375, -375, 1250, 625;
693, -981, 750, -375, 1875, 625;
|
|
MAPLE
|
# This will generate the sequence as coefficients of pseudo polynomials
# up to a constant multiple.
a[0] := f(x):
for i to 10 do
a[i] := simplify(x^(1/5)*(diff(a[i-1], x$1)))
end do;
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|