A393479 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.

1, 1, 8, 216, 29376, 5239107, 2399999949, 1795800631122, 1307922911815122, 1292282305350152670, 9654542873822353608, 10113180951218495294628, 44399995821087166058118012, 397905961067265907140056917272, 3443726262728475072600035928009768, 26318962130511885810773470539946370280

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..15.

Example

a(4) = 29376:
  [1, 2,  3,  4]
  [2, 4,  6,  8]
  [3, 6,  9, 21]
  [4, 8, 21, 61]

Maple

rev:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
f:= proc(n) LinearAlgebra:-Permanent(Matrix(n, n, (i, j) -> rev(i*j))) end proc:
f(0):= 1:
map(f, [$0..20]); # Robert Israel, Feb 16 2026

Mathematica

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

Prog

(PARI) a(n) = matpermanent(matrix(n, n, i, j, fromdigits(Vecrev(digits(i*j))))); \\ Michel Marcus, Feb 16 2026

Crossrefs

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

Sequence in context: A226524 A359412 A115964 * A245591 A247539 A188680

Adjacent sequences: A393476 A393477 A393478 * A393480 A393481 A393482

Keyword

nonn,base

Author

Stefano Spezia, Feb 16 2026

Status

approved