OFFSET
0,2
COMMENTS
LINKS
Mircea Merca, Some experiments with complete and elementary symmetric functions, Periodica Mathematica Hungarica, 69 (2014), 182-189.
FORMULA
G.f.: 1/Product_{j=1..8} 1-8!*x/j.
a(n) = -((8!)^n) * Sum_{j=1..8} (-1)^j*binomial(8, j)/j^n, n>=0.
a(n) = A112492(n+7, 8), n>=0.
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, (k+1)^(n-k)*T[n-1, k-1] +k!*T[n-1, k]]; (* T = A112492 *)
Table[T[n+7, 7], {n, 0, 30}] (* G. C. Greubel, Jul 24 2023 *)
PROG
(PARI) a(n) = -((8!)^n)*sum(j=1, 8, ((-1)^j)*binomial(8, j)/j^n); \\ Michel Marcus, Apr 28 2020
(Magma)
A111888:= func< n | (-1)*Factorial(8)^n*(&+[(-1)^j*Binomial(8, j)/j^n : j in [1..8]]) >;
[A111888(n): n in [0..30]]; // G. C. Greubel, Jul 24 2023
(SageMath)
@CachedFunction
def T(n, k): # T = A112492
if (k==0 or k==n): return 1
else: return (k+1)^(n-k)*T(n-1, k-1) + factorial(k)*T(n-1, k)
def A111888(n): return T(n+7, 7)
[A111888(n) for n in range(31)] # G. C. Greubel, Jul 24 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 12 2005
STATUS
approved