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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 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

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