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A111599 Lah numbers: n!*binomial(n-1,8)/9!. 1
1, 90, 4950, 217800, 8494200, 309188880, 10821610800, 371026656000, 12614906304000, 428906814336000, 14668613050291200, 506733905373696000, 17735686688079360000, 630299019222512640000, 22780807409042242560000 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,2

REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.

LINKS

Table of n, a(n) for n=9..23.

FORMULA

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

MAPLE

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

MATHEMATICA

Table[n!*Binomial[n-1, 8]/9!, {n, 9, 30}] (* Wesley Ivan Hurt, Dec 10 2013 *)

CROSSREFS

Column 9 of unsigned A008297 and A111596. Column 8: A111598.

Sequence in context: A221893 A197194 A281580 * A111783 A075918 A076010

Adjacent sequences:  A111596 A111597 A111598 * A111600 A111601 A111602

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Aug 23 2005

STATUS

approved

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Last modified February 22 12:42 EST 2020. Contains 332136 sequences. (Running on oeis4.)