A321511 Number of alternating sign n X n matrices excluding permutation matrices.

0, 0, 0, 1, 18, 309, 6716, 213308, 10809896, 911472580, 129530643900, 31095704935575, 12611311380675900, 8639383512070631700, 9995541355360989190800, 19529076234659969430529200, 64427185703425668434106855840, 358869201916137601091798728321296

Offset: 0

Author

Wendy Appleby, Nov 11 2018

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..93
• Paul Barry, Centered polygon numbers, heptagons and nonagons, and the Robbins numbers, arXiv:2104.01644 [math.CO], 2021.
• Paul Barry, Extensions of Riordan Arrays and Their Applications, Mathematics (2025) Vol. 13, No. 2, 242. See p. 8.

Crossrefs

Cf. A005130.

Programs

Mathematica

a[n_] := Product[(3 k + 1)!/(n + k)!, {k, 0, n-1}] - n!; a /@ Range[0, 17] (* Giovanni Resta, Nov 20 2018 *)

Formula

a(n) = A005130(n) - n!