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A111599
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Lah numbers: a(n) = n!*binomial(n-1,8)/9!.
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1
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1, 90, 4950, 217800, 8494200, 309188880, 10821610800, 371026656000, 12614906304000, 428906814336000, 14668613050291200, 506733905373696000, 17735686688079360000, 630299019222512640000, 22780807409042242560000
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OFFSET
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9,2
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REFERENCES
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Louis Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
John Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.
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LINKS
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FORMULA
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E.g.f.: ((x/(1-x))^9)/9!.
a(n) = (n!/9!)*binomial(n-1, 9-1).
If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..k} binomial(k,j)*Stirling1(n,k)*Stirling2(j,i)*x^(k-j)), then a(n) = (-1)^(n-1)*f(n,9,-9), n >= 9. - Milan Janjic, Mar 01 2009
Sum_{n>=9} 1/a(n) = 564552*(Ei(1) - gamma) - 264528*e - 873657/35, where Ei(1) = A091725, gamma = A001620, and e = A001113.
Sum_{n>=9} (-1)^(n+1)/a(n) = 28393416*(gamma - Ei(-1)) - 16938720/e - 573537159/35, where Ei(-1) = -A099285. (End)
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MAPLE
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part_ZL:=[S, {S=Set(U, card=r), U=Sequence(Z, card>=1)}, labeled]: seq(count(subs(r=9, part_ZL), size=m), m=9..23) ; # Zerinvary Lajos, Mar 09 2007
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MATHEMATICA
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CROSSREFS
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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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