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A111886
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Sixth column of triangle A112492 (inverse scaled Pochhammer symbols).
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3
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1, 1764, 1942416, 1744835904, 1413470290176, 1083688832185344, 806595068762689536, 590914962115587293184, 429295503918929370218496, 310518802877016005311463424, 224098118280955193084850733056
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OFFSET
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0,2
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COMMENTS
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Also continuation of family of differences of reciprocals of unity. See A001242 and triangle A008969.
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LINKS
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FORMULA
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G.f.: 1/Product_{j=1..6} (1-6!*x/j).
a(n) = -((6!)^n)*Sum_{j=1..6} (-1)^j*binomial(6, j)/j^n, n >= 0.
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = -((6!)^n)*sum(j=1, 6, (-1)^j*binomial(6, j)/j^n); \\ Michel Marcus, Apr 28 2020
(Magma)
A111886:= func< n | (-1)*Factorial(6)^n*(&+[(-1)^j*Binomial(6, j)/j^n : j in [1..6]]) >;
(SageMath)
@CachedFunction
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)
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CROSSREFS
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Also right-hand column 5 in triangle A008969.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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