cp's OEIS Frontend

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

%I A111887 #18 Jul 25 2023 09:15:13
%S A111887 1,13068,104587344,673781602752,3878864920694016,21006340945438768128,
%T A111887 110019668725577574273024,565858042127972959667208192,
%U A111887 2882220940619488483325345857536,14605752814655604919042956624396288
%N A111887 Seventh column of triangle A112492 (inverse scaled Pochhammer symbols).
%C A111887 Also continuation of family of differences of reciprocals of unity. See A001242, A111886 and triangle A008969.
%H A111887 G. C. Greubel, <a href="/A111887/b111887.txt">Table of n, a(n) for n = 0..250</a>
%H A111887 Mircea Merca, <a href="https://www.researchgate.net/publication/264664262_Some_experiments_with_complete_and_elementary_symmetric_functions">Some experiments with complete and elementary symmetric functions</a>, Periodica Mathematica Hungarica, 69 (2014), 182-189.
%F A111887 G.f.: 1/Product_{j=1..7} 1-7!*x/j.
%F A111887 a(n) = -((7!)^n) * Sum_{j=1..7} (-1)^j*binomial(7, j)/j^n, n>=0.
%F A111887 a(n) = A112492(n+6, 7), n>=0.
%t A111887 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 *)
%t A111887 Table[T[n+6,6], {n,0,30}] (* _G. C. Greubel_, Jul 24 2023 *)
%o A111887 (PARI) a(n) = -((7!)^n)*sum(j=1, 7, ((-1)^j)*binomial(7, j)/j^n); \\ _Michel Marcus_, Apr 28 2020
%o A111887 (Magma)
%o A111887 A111887:= func< n | (-1)*Factorial(7)^n*(&+[(-1)^j*Binomial(7,j)/j^n : j in [1..7]]) >;
%o A111887 [A111887(n): n in [0..30]]; // _G. C. Greubel_, Jul 24 2023
%o A111887 (SageMath)
%o A111887 @CachedFunction
%o A111887 def T(n,k): # T = A112492
%o A111887     if (k==0 or k==n): return 1
%o A111887     else: return (k+1)^(n-k)*T(n-1,k-1) + factorial(k)*T(n-1,k)
%o A111887 def A111887(n): return T(n+6,6)
%o A111887 [A111887(n) for n in range(31)] # _G. C. Greubel_, Jul 24 2023
%Y A111887 Also right-hand column 6 in triangle A008969.
%Y A111887 Cf. A001242, A111886, A112492.
%K A111887 nonn,easy
%O A111887 0,2
%A A111887 _Wolfdieter Lang_, Sep 12 2005