A275025 Number of pairs of functions (f,g) on [n] such that fg is an idempotent.

1, 1, 14, 411, 21208, 1703145, 195285456, 30113813863, 5985071842688, 1485696848042385, 449588756524844800, 162668114715527356551, 69259775641873646754816, 34243366782512243213286169, 19439795735713938153732810752, 12549399357405863545478828022375

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: A353609 A222904 A239785 * A236156 A258392 A269504

Adjacent sequences: A275022 A275023 A275024 * A275026 A275027 A275028

Keyword

nonn

Author

David Einstein, Nov 12 2016

Status

approved