A321511 - OEIS

%I #15 Feb 19 2025 12:11:08

%S 0,0,0,1,18,309,6716,213308,10809896,911472580,129530643900,

%T 31095704935575,12611311380675900,8639383512070631700,

%U 9995541355360989190800,19529076234659969430529200,64427185703425668434106855840,358869201916137601091798728321296

%N Number of alternating sign n X n matrices excluding permutation matrices.

%H Michael De Vlieger, <a href="/A321511/b321511.txt">Table of n, a(n) for n = 0..93</a>

%H Paul Barry, <a href="https://arxiv.org/abs/2104.01644">Centered polygon numbers, heptagons and nonagons, and the Robbins numbers</a>, arXiv:2104.01644 [math.CO], 2021.

%H Paul Barry, <a href="https://doi.org/10.3390/math13020242">Extensions of Riordan Arrays and Their Applications</a>, Mathematics (2025) Vol. 13, No. 2, 242. See p. 8.

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

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

%Y Cf. A005130.

%K nonn

%O 0,5

%A _Wendy Appleby_, Nov 11 2018