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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

N. J. A. Sloane.

EXTENSIONS

More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 2/12/01

STATUS

approved

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Last modified May 29 07:35 EDT 2017. Contains 287244 sequences.