A111598 Lah numbers: a(n) = n!*binomial(n-1,7)/8!.

1, 72, 3240, 118800, 3920400, 122316480, 3710266560, 111307996800, 3339239904000, 100919250432000, 3088129063219200, 96012739965542400, 3040403432242176000, 98228418580131840000, 3241537813144350720000

Offset

8,2

References

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

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

Links

G. C. Greubel, Table of n, a(n) for n = 8..440

Formula

E.g.f.: ((x/(1-x))^8)/8!.

a(n) = (n!/8!)*binomial(n-1, 8-1).

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*f(n,8,-8), (n>=8). - Milan Janjic, Mar 01 2009

From Amiram Eldar, May 02 2022: (Start)

Sum_{n>=8} 1/a(n) = 61096*(gamma - Ei(1)) + 54544*e - 338732/5, where gamma = A001620, Ei(1) = A091725 and e = A001113.

Sum_{n>=8} (-1)^n/a(n) = 2107448*(gamma - Ei(-1)) - 1257760/e - 6080436/5, where Ei(-1) = -A099285. (End)

Mathematica

Table[(n-8)!*Binomial[n-1, 7]*Binomial[n, 8], {n, 8, 35}] (* G. C. Greubel, May 10 2021 *)

Prog

(Magma) [Factorial(n-8)*Binomial(n, 8)*Binomial(n-1, 7): n in [8..35]]; // G. C. Greubel, May 10 2021
(Sage) [factorial(n-8)*binomial(n, 8)*binomial(n-1, 7) for n in (8..35)] # G. C. Greubel, May 10 2021

Crossrefs

Column 8 of unsigned A008297 and A111596.

Column 7 of A111597.

Cf. A001113, A001620, A091725, A099285.

Sequence in context: A173192 A004366 A004389 * A116312 A111782 A060507

Adjacent sequences: A111595 A111596 A111597 * A111599 A111600 A111601

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 23 2005

Status

approved