A121080 a(n) = Sum_{i=0..n} C(n,i)^2*i!*4^i + (1-2^n)*2^(n-1)*n!.

1, 4, 37, 541, 10625, 258661, 7464625, 248318309, 9339986689, 391569431365, 18095180332721, 913513359466885, 50008961524486849, 2950209091316054309, 186558089772409191985, 12587159519294553302821, 902488447534988078746625, 68518909362619336345906309

Offset: 0

Author

N. J. A. Sloane, Aug 11 2006

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..363
• Joël Gay, Representation of Monoids and Lattice Structures in the Combinatorics of Weyl Groups, Doctoral Thesis, Discrete Mathematics [cs.DM], Université Paris-Saclay, 2018.
• Z. Li, Z. Li and Y. Cao, Enumeration of symplectic and orthogonal injective partial transformations, Discrete Math., 306 (2006), 1781-1787.

Crossrefs

Cf. A102773, A121079.

Programs

Mathematica

Array[Sum[Binomial[#, i]^2*i!*4^i, {i, 0, #}] + (1 - 2^#)*2^(# - 1)*#! &, 18, 0] (* Michael De Vlieger, Nov 28 2018 *)

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