A375231 Interleaving A006040 and A228229.

1, 1, 3, 9, 19, 82, 229, 1313, 4581, 32826, 137431, 1181737, 5772103, 57905114, 323237769, 3705927297, 23273119369, 300180111058, 2094580743211, 30018011105801, 230403881753211, 3632179343801922, 30413312391423853, 523033825507476769, 4744476733062121069, 88392716510763573962

Offset: 0

Author

Stefano Spezia, Aug 06 2024

Keywords

• nonn

Comments

Conjecture: a(n) is the permanent of the n X n matrix whose generic element is given by M_{i,j} = 1 if i = j or i + j = 1 (mod 2), with i,j in [n].

Crossrefs

Cf. A006040, A078126 (determinant), A228229.

Programs

Mathematica

A006040[n_]:=Sum[(n!/(n - k)!)^2, {k, 0, n}]; A228229[n_]:= n!*(n + 1)!*Sum[ 1/(k!*(k + 1)!),{k,0,n}]; a[n_]:=If[OddQ[n],A006040[(n+1)/2],A228229[n/2]]; Array[a,26,0]

Formula

a(n) = A006040((n+1)/2) for odd n.

a(n) = A228229(n/2) for even n.