cp's OEIS Frontend

A371153 a(n) is the permanent of the 2n+1 X 2n+1 matrix P(2n+1) defined by P[1,j] = 1, P[i,j] = i-1 if i<=j, and P[i,i] = i-n-1 otherwise with 1 <= i,j <= 2n+1.

%I A371153 #30 Mar 14 2024 09:03:13
%S A371153 1,-3,185,-55307,49980969,-106782742099,462446644072153,
%T A371153 -3649813053096346875,48540310969531346254217,
%U A371153 -1024268653171975469599364291,32694499032613728282606987622521,-1518591968826504411972243578217645163,99392870823564324693001427592486103515625
%N A371153 a(n) is the permanent of the 2n+1 X 2n+1 matrix P(2n+1) defined by P[1,j] = 1, P[i,j] = i-1 if i<=j, and P[i,i] = i-n-1 otherwise with 1 <= i,j <= 2n+1.
%C A371153 The matrices P(2n) have permanent equal to zero.
%e A371153 a(3) = -55307:
%e A371153    1,  1,  1,  1,  1,  1, 1;
%e A371153   -6,  1,  1,  1,  1,  1, 1;
%e A371153   -5, -5,  2,  2,  2,  2, 2;
%e A371153   -4, -4, -4,  3,  3,  3, 3;
%e A371153   -3, -3, -3, -3,  4,  4, 4;
%e A371153   -2, -2, -2, -2, -2,  5, 5;
%e A371153   -1, -1, -1, -1, -1, -1, 6.
%t A371153 b[n_]:=Permanent[Table[If[i==1, 1, If[i<=j, i-1, i-n-1]], {i, n}, {j, n}]]; a[n_]:=b[2n+1]; Array[a, 10,0]
%Y A371153 Cf. A000169, A005408, A084849 (trace), A085530 (determinant).
%K A371153 sign
%O A371153 0,2
%A A371153 _Stefano Spezia_, Mar 13 2024