A038720 a(n) = (n+3)*n!/2.

2, 5, 18, 84, 480, 3240, 25200, 221760, 2177280, 23587200, 279417600, 3592512000, 49816166400, 741015475200, 11769069312000, 198766503936000, 3556874280960000, 67224923910144000, 1338096104497152000, 27978373094031360000, 613091306060513280000

Offset

1,1

Comments

Next-to-last diagonal of A038719.

a(n-1) is the sum of the n-th entries in all cycles of all permutations of [n]. a(2) = 5 because the sum of the third entries in all cycles of all permutations of [3] ((123), (132), (12)(3), (13)(2), (1)(23), (1)(2)(3)) is 3+2+0+0+0+0 = 5. - Alois P. Heinz, May 03 2017

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Rajesh Kumar Mohapatra and Tzung-Pei Hong, On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences, Mathematics (2022) Vol. 10, No. 7, 1161.

R. B. Nelsen and H. Schmidt, Jr., Chains in power sets, Math. Mag., 64 (1991), 23-31.

Index entries for sequences related to posets.

Formula

a(n) = A052572(n)/2.

a(n) = A214178(n+3,n). - Reinhard Zumkeller, Jul 08 2012

G.f.: Sum_{n>=1} ( (n+1)*x/(1 + (n+1)*x) )^n. - Paul D. Hanna, Jan 02 2013

E.g.f.: 1/(1-x)+1/(2*(x-1)^2)-3/2. - Alois P. Heinz, May 04 2017

From Amiram Eldar, Dec 11 2022: (Start)

Sum_{n>=1} 1/a(n) = 2*e - 14/3.

Sum_{n>=1} (-1)^(n+1)/a(n) = 10/e - 10/3. (End)

Mathematica

Array[(# + 3) #!/2 &, 21] (* Michael De Vlieger, Apr 28 2022 *)

Prog

(Haskell)
import Data.List (transpose)
a038720 n = a038720_list !! (n-1)
a038720_list = (transpose $ map reverse a038719_tabl) !! 1
-- Reinhard Zumkeller, Jul 08 2012

Crossrefs

Cf. A038719, A038721, A052572, A214178.

Main diagonal of A285793.

Sequence in context: A118187 A307773 A332776 * A157312 A175847 A089412

Adjacent sequences: A038717 A038718 A038719 * A038721 A038722 A038723

Keyword

nonn,easy

Author

N. J. A. Sloane, May 02 2000

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), May 09 2000.

Status

approved