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A038720 a(n) = (n+3)*n!/2. 13
2, 5, 18, 84, 480, 3240, 25200, 221760, 2177280, 23587200, 279417600, 3592512000, 49816166400, 741015475200, 11769069312000, 198766503936000, 3556874280960000, 67224923910144000, 1338096104497152000, 27978373094031360000, 613091306060513280000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Next-to-last diagonal of A038719.

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

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

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

Half of A052572.

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

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

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Last modified March 3 13:41 EST 2021. Contains 341762 sequences. (Running on oeis4.)