%I #12 Nov 28 2018 15:29:28
%S 2,7,57,757,13889,322021,8962225,289928549,10666353409,439225736005,
%T 19999574572721,997265831223685,54028099173536449,3159178743189436709,
%U 198259676112757095985,13289233274778582230821,947420482287986880154625,71574264415491967142194309
%N a(n) = Sum_{i=0..n} C(n,i)^2*i!*4^i + 2^n*n!.
%H Michael De Vlieger, <a href="/A121079/b121079.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, #}] + 2^#*#! &, 18, 0] (* _Michael De Vlieger_, Nov 28 2018 *)
%o (PARI) a(n) = 2^n*n! + sum(i=0, n, binomial(n,i)^2*i!*4^i); \\ _Michel Marcus_, May 31 2018
%Y Cf. A102773, A121080.
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Aug 11 2006