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A372343 a(n) is the permanent of the n X n matrix whose element (i,j) equals PS(i+2,j), where PS(r,c) is the Legendre-Stirling number of the second kind (A071951).

%I A372343 #6 Apr 28 2024 11:33:29
%S A372343 1,12,2448,2900160,3335369728,16355507060736,202873109257748480,
%T A372343 5520786912662854893568,304515605038514679874846720,
%U A372343 31568014831906551177163996921856,5785425274398818300907155436515360768,1783302045417843100606023721285336961122304,886715046570481808433485979311322483302619676672
%N A372343 a(n) is the permanent of the n X n matrix whose element (i,j) equals PS(i+2,j), where PS(r,c) is the Legendre-Stirling number of the second kind (A071951).
%H A372343 G. E. Andrews, W. Gawronski, and L. L. Littlejohn, <a href="https://doi.org/10.1016/j.disc.2011.02.028">The Legendre-Stirling Numbers</a>, Discrete Mathematics, Volume 311, Issue 14, 28 July 2011, Pages 1255-1272.
%t A372343 PS[n_,k_]:=Sum[(-1)^(r+k)(2r+1)(r^2+r)^n/((r+k+1)!(k-r)!),{r,0,k}]; a[0]:=1; a[n_]:=Permanent[Table[PS[i+2,j],{i,n},{j,n}]]; Array[a,13,0]
%Y A372343 Cf. A069135 (determinant), A071951.
%K A372343 nonn
%O A372343 0,2
%A A372343 _Stefano Spezia_, Apr 28 2024