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A111887 Seventh column of triangle A112492 (inverse scaled Pochhammer symbols). 2
1, 13068, 104587344, 673781602752, 3878864920694016, 21006340945438768128, 110019668725577574273024, 565858042127972959667208192, 2882220940619488483325345857536, 14605752814655604919042956624396288 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Also continuation of family of differences of reciprocals of unity. See A001242, A111886 and triangle A008969.
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..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.
Sequence in context: A256730 A234329 A165679 * A249495 A235335 A184768
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 12 2005
STATUS
approved

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Last modified June 13 09:43 EDT 2024. Contains 373383 sequences. (Running on oeis4.)