login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A275025 Number of pairs of functions (f,g) on [n] such that fg is an idempotent. 1
1, 1, 14, 411, 21208, 1703145, 195285456, 30113813863, 5985071842688, 1485696848042385, 449588756524844800, 162668114715527356551, 69259775641873646754816, 34243366782512243213286169, 19439795735713938153732810752, 12549399357405863545478828022375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100

David Einstein, Pseudoinverses on finite sets

FORMULA

a(n) = Sum_{k = 0..n} ((n!)^2/k!) Sum_{j = 0..n-k} 1/(j!(n-k-j)!) Sum_{l = 0..j} k^(n-k-j+l) n^(n-k-l) stirling2(j,l)/(n-k-l)!.

EXAMPLE

The fourteen pairs of functions on [2] are: ([1,1], [1,1]), ([1,1], [1,2]), ([1,1], [2,1]), ([1,1], [2,2]), ([1,2], [1,1]), ([1,2], [1,2]), ([1,2], [2,2]), ([2,1], [1,1]), ([2,1], [2,1]), ([2,1], [2,2]), ([2,2], [1,1]), ([2,2], [1,2]), ([2,2], [2,1]), ([2,2], [2,2]).

CROSSREFS

Cf. A239768, A000248.

Sequence in context: A041364 A222904 A239785 * A236156 A258392 A269504

Adjacent sequences:  A275022 A275023 A275024 * A275026 A275027 A275028

KEYWORD

nonn

AUTHOR

David Einstein, Nov 12 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 23 16:08 EDT 2021. Contains 345402 sequences. (Running on oeis4.)