A393479 - OEIS

%I #13 Feb 20 2026 15:54:51

%S 1,1,8,216,29376,5239107,2399999949,1795800631122,1307922911815122,

%T 1292282305350152670,9654542873822353608,10113180951218495294628,

%U 44399995821087166058118012,397905961067265907140056917272,3443726262728475072600035928009768,26318962130511885810773470539946370280

%N a(n) is the permanent of the n X n symmetric matrix M(n) whose generic element M[i,j] is equal to the digit reversal of i*j.

%C The matrix M(n) is nonsingular only for n in {1, 5, 6, 7, 8, 9}.

%e a(4) = 29376:

%e   [1, 2,  3,  4]

%e   [2, 4,  6,  8]

%e   [3, 6,  9, 21]

%e   [4, 8, 21, 61]

%p rev:= proc(n) local L,i;

%p   L:= convert(n,base,10);

%p   add(L[-i]*10^(i-1),i=1..nops(L))

%p end proc:

%p f:= proc(n) LinearAlgebra:-Permanent(Matrix(n,n,(i,j) -> rev(i*j))) end proc:

%p f(0):= 1:

%p map(f, [$0..20]); # _Robert Israel_, Feb 16 2026

%t a[n_]:=Permanent[Table[IntegerReverse[i*j],{i,n},{j,n}]]; Join[{1},Array[a,15]]

%o (PARI) a(n) = matpermanent(matrix(n, n, i, j, fromdigits(Vecrev(digits(i*j))))); \\ _Michel Marcus_, Feb 16 2026

%Y Cf. A003991, A004086, A353933, A362073, A391365, A393480 (hafnian).

%K nonn,base

%O 0,3

%A _Stefano Spezia_, Feb 16 2026