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 A001755 Lah numbers: n! C(n-1,3)/4!. (Formerly M5096 N2207) 7
 1, 20, 300, 4200, 58800, 846720, 12700800, 199584000, 3293136000, 57081024000, 1038874636800, 19833061248000, 396661224960000, 8299373322240000, 181400588328960000, 4135933413900288000, 98228418580131840000, 2426819753156198400000, 62288373664342425600000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,2 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 156. J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 4..100 FORMULA E.g.f.: ((x/(1-x))^4)/4!. 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*f(n,4,-4), (n>=4). [Milan Janjic, Mar 01 2009] MAPLE A001755 := n-> n!*binomial(n-1, 3)/4!; MATHEMATICA Table[n! Binomial[n - 1, 3]/4!, {n, 4, 25}] (* T. D. Noe, Aug 10 2012 *) PROG (Sage) [binomial(n, 4)*factorial (n-1)/6 for n in xrange(4, 21)] # [From Zerinvary Lajos, Jul 07 2009] CROSSREFS Column 4 of A008297. Cf. A053495. Column m=4 of unsigned triangle A111596. Sequence in context: A202270 A053541 A004345 * A016190 A016188 A006300 Adjacent sequences:  A001752 A001753 A001754 * A001756 A001757 A001758 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/12/01 STATUS approved

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