A111887 Seventh column of triangle A112492 (inverse scaled Pochhammer symbols).

1, 13068, 104587344, 673781602752, 3878864920694016, 21006340945438768128, 110019668725577574273024, 565858042127972959667208192, 2882220940619488483325345857536, 14605752814655604919042956624396288

Offset

0,2

Comments

Also continuation of family of differences of reciprocals of unity. See A001242, A111886 and triangle A008969.

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Mircea Merca, Some experiments with complete and elementary symmetric functions, Periodica Mathematica Hungarica, 69 (2014), 182-189.

Formula

G.f.: 1/Product_{j=1..7} 1-7!*x/j.

a(n) = -((7!)^n) * Sum_{j=1..7} (-1)^j*binomial(7, j)/j^n, n>=0.

a(n) = A112492(n+6, 7), 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+6, 6], {n, 0, 30}] (* G. C. Greubel, Jul 24 2023 *)

Prog

(PARI) a(n) = -((7!)^n)*sum(j=1, 7, ((-1)^j)*binomial(7, j)/j^n); \\ Michel Marcus, Apr 28 2020
(Magma)
A111887:= func< n | (-1)*Factorial(7)^n*(&+[(-1)^j*Binomial(7, j)/j^n : j in [1..7]]) >;
[A111887(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 A111887(n): return T(n+6, 6)
[A111887(n) for n in range(31)] # G. C. Greubel, Jul 24 2023

Crossrefs

Also right-hand column 6 in triangle A008969.

Cf. A001242, A111886, A112492.

Sequence in context: A256730 A234329 A165679 * A249495 A235335 A184768

Adjacent sequences: A111884 A111885 A111886 * A111888 A111889 A111890

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 12 2005

Status

approved