|
|
A191422
|
|
Expansion of e.g.f. (1 + x + x^2)^x.
|
|
2
|
|
|
1, 0, 2, 3, -4, 90, -126, -840, 21104, -137592, -88920, 15741000, -197234808, 535289040, 25582565904, -522317151720, 3223601137920, 75590725210560, -2388641226278976, 23718732310200960, 361277667059425920
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: (1 + x + x^2)^x.
a(n) = n!*Sum_{m=1..n} Sum_{k=0..n-2*m} Stirling1(m+k, m)*binomial(m+k, n-2*m-k)/(m+k)! for n > 0, a(0)=1.
|
|
MAPLE
|
S:= series((1+x+x^2)^x, x, 41):
|
|
PROG
|
(Maxima)
a(n):=if n=0 then 1 else (sum(sum((stirling1(m+k, m)*binomial(m+k, n-2*m-k))/(m+k)!, k, 0, n-2*m), m, 1, n))*n!;
(PARI) my(x='x+O('x^30)); Vec(serlaplace((1+x+x^2)^x))) \\ Michel Marcus, Apr 28 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|