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%I #12 Nov 28 2018 15:29:45
%S 1,4,37,541,10625,258661,7464625,248318309,9339986689,391569431365,
%T 18095180332721,913513359466885,50008961524486849,2950209091316054309,
%U 186558089772409191985,12587159519294553302821,902488447534988078746625,68518909362619336345906309
%N a(n) = Sum_{i=0..n} C(n,i)^2*i!*4^i + (1-2^n)*2^(n-1)*n!.
%H Michael De Vlieger, <a href="/A121080/b121080.txt">Table of n, a(n) for n = 0..363</a>
%H Joël Gay, <a href="https://tel.archives-ouvertes.fr/tel-01861199">Representation of Monoids and Lattice Structures in the Combinatorics of Weyl Groups</a>, Doctoral Thesis, Discrete Mathematics [cs.DM], Université Paris-Saclay, 2018.
%H Z. Li, Z. Li and Y. Cao, <a href="https://doi.org/10.1016/j.disc.2006.03.047">Enumeration of symplectic and orthogonal injective partial transformations</a>, Discrete Math., 306 (2006), 1781-1787.
%t Array[Sum[Binomial[#, i]^2*i!*4^i, {i, 0, #}] + (1 - 2^#)*2^(# - 1)*#! &, 18, 0] (* _Michael De Vlieger_, Nov 28 2018 *)
%o (PARI) a(n) = (1-2^n)*2^(n-1)*n! + sum(i=0, n, binomial(n,i)^2*i!*4^i); \\ _Michel Marcus_, May 31 2018
%Y Cf. A102773, A121079.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Aug 11 2006
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