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.
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
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