OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n+3} n^k*(Stirling2(n+3,k) - 3*Stirling2(n+2,k) + 2*Stirling2(n+1,k)). - Andrew Howroyd, Oct 20 2020
a(n) = Sum_{k=0..n} n^(k+3)*A143495(n+3, k+3). - Peter Luschny, Oct 21 2020
EXAMPLE
a(3) = 7371 = (1/e^3) * Sum_{j>=3} j^3 * 3^j / factorial(j-3).
MAPLE
seq(add(n^(k+3)*A143495(n+3, k+3), k = 0..n), n = 0..17); # Peter Luschny, Oct 21 2020
MATHEMATICA
a[n_] := Exp[-n] * Sum[j^n * n^j/(j - 3)!, {j, 3, Infinity}]; Array[a, 17, 0] (* Amiram Eldar, Oct 20 2020 *)
PROG
(SageMath) # Increase precision for larger n!
R = RealField(100)
t = 3
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)
print(sol) # Peter Luschny, Oct 20 2020
(PARI) a(n)={sum(k=0, n+3, n^k*(stirling(n+3, k, 2) - 3*stirling(n+2, k, 2) + 2*stirling(n+1, k, 2)))} \\ Andrew Howroyd, Oct 20 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Pedro Caceres, Oct 20 2020
STATUS
approved