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 A275025 Number of pairs of functions (f,g) on [n] such that fg is an idempotent. 1

%I

%S 1,1,14,411,21208,1703145,195285456,30113813863,5985071842688,

%T 1485696848042385,449588756524844800,162668114715527356551,

%U 69259775641873646754816,34243366782512243213286169,19439795735713938153732810752,12549399357405863545478828022375

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

%H Alois P. Heinz, <a href="/A275025/b275025.txt">Table of n, a(n) for n = 0..100</a>

%H David Einstein, <a href="https://github.com/deinst/oeis-function-identities/blob/master/Pseudoinverses.ipynb">Pseudoinverses on finite sets</a>

%F 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)!.

%e 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]).

%Y Cf. A239768, A000248.

%K nonn

%O 0,3

%A _David Einstein_, Nov 12 2016

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Last modified July 31 15:25 EDT 2021. Contains 346374 sequences. (Running on oeis4.)