A111600 Lah numbers: a(n) = n!*binomial(n-1,9)/10!.

1, 110, 7260, 377520, 17177160, 721440720, 28857628800, 1121325004800, 42890681433600, 1629845894476800, 61934143990118400, 2364758225077248000, 91043191665474048000, 3543681152517682176000, 139722285442125754368000

Offset: 10

Author

Wolfdieter Lang, Aug 23 2005

Keywords

• nonn
• easy

References

• Louis Comtet, Advanced Combinatorics, Reidel, 1974, p. 156.
• John Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 44.

Crossrefs

Column 10 of unsigned A008297 and A111596.

Column 9: A111599.

Cf. A001113, A001620, A091725, A099285.

Programs

Mathematica

Table[n! * Binomial[n - 1, 9]/10!, {n, 10, 25}] (* Amiram Eldar, May 02 2022 *)

Formula

E.g.f.: ((x/(1-x))^10)/10!.

a(n) = (n!/10!)*binomial(n-1, 10-1).

If we define f(n,i,x) = Sum_{k=1..n} Sum_{j=i..k} binomial(k,j) * Stirling1(n,k) * Stirling2(j,i)*x^(k-j) then a(n) = (-1)^n*f(n,10,-10), (n>=10). - Milan Janjic, Mar 01 2009

From Amiram Eldar, May 02 2022: (Start)

Sum_{n>=10} 1/a(n) = 5086710*(gamma - Ei(1)) + 50940*e + 91914449/14, where gamma = A001620, Ei(1) = A091725 and e = A001113.

Sum_{n>=10} (-1)^n/a(n) = 413689770*(gamma - Ei(-1)) - 246749400/e - 3342795017/14, where Ei(-1) = -A099285. (End)