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Search: id:A111599
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| A111599 |
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Lah numbers: n!*binomial(n-1,8)/9!. |
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+0
2
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| 1, 90, 4950, 217800, 8494200, 309188880, 10821610800, 371026656000, 12614906304000, 428906814336000, 14668613050291200, 506733905373696000, 17735686688079360000, 630299019222512640000, 22780807409042242560000
(list; graph; listen)
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OFFSET
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9,2
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.
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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(sum(binomial(k,j)*stirling1(n,k)*stirling2(j,i)*x^(k-j),j=i..k),k=i..n) then a(n)=(-1)^(n-1)*f(n,9,-9), (n>=9). [From Milan R. Janjic (agnus(AT)blic.net), Mar 01 2009]
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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 (zerinvarylajos(AT)yahoo.com), Mar 09 2007
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CROSSREFS
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Column 9 of unsigned A008297 and A111596. Column 8: A111598.
Sequence in context: A017806 A035740 A017753 this_sequence A111783 A075918 A076010
Adjacent sequences: A111596 A111597 A111598 this_sequence A111600 A111601 A111602
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 23 2005
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