|
|
A332188
|
|
a(n) = (1/e^n) * Sum_{j>=2} j^n * n^j / (j-2)!.
|
|
0
|
|
|
0, 3, 72, 1557, 36928, 986550, 29641608, 994006209, 36887753216, 1502798312547, 66730937637400, 3209318261685690, 166242143849148864, 9229638177763268395, 546842961612529341032, 34443269219453881669425
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n+2} n^k*(Stirling2(n+2,k) - Stirling2(n+1,k)). [Thanks to Andrew Howroyd for his example in A338282]
|
|
EXAMPLE
|
a(3) = 1557 = (1/e^3) * Sum_{j>=2} j^3 * 3^j / factorial(j-2).
|
|
MATHEMATICA
|
a[n_] := Sum[n^k*(StirlingS2[n + 2, k] - StirlingS2[n + 1, k]), {k, 2, n + 2}]; Array[a, 16, 0] (* Amiram Eldar, Oct 30 2020 *)
|
|
PROG
|
(SageMath) # Increase precision for larger n!
R = RealField(100)
t = 2
sol = [0]*18
for n in range(0, 18):
suma = R(0)
for j in range(t, 1000):
suma += (j^n * n^j) / factorial(j - t)
suma *= exp(-n)
sol[n] = round(suma)
(PARI) a(n) = sum(k=0, n+2, n^k*(stirling(n+2, k, 2) - stirling(n+1, k, 2))); \\ Michel Marcus, Oct 30 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|