A393480 a(n) is the hafnian of the 2n X 2n symmetric matrix whose generic element M[i,j] is equal to the digit reversal of i*j.

1, 2, 90, 19089, 16173999, 1414293534, 2802869044173, 22551947376101055, 213300662882056463637, 4552155569894863857602445, 6356674411068592198597993830, 112761457122054803122314301920246

Offset

0,2

Links

Table of n, a(n) for n=0..11.

Wikipedia, Hafnian.

Wikipedia, Symmetric matrix.

Example

a(2) = 90:
  [1, 2,  3,  4]
  [2, 4,  6,  8]
  [3, 6,  9, 21]
  [4, 8, 21, 61]

Mathematica

M[i_, j_, n_] :=IntegerReverse[i*j ]; a[n_] := Sum[Product[M[Part[PermutationList[s, 2 n], 2 i - 1], Part[PermutationList[s, 2 n], 2 i], 2 n], {i, n}], {s, SymmetricGroup[2 n] // GroupElements}]/(n!*2^n); Array[a, 6, 0]

Prog

(PARI) tm(n) = matrix(n, n, i, j, fromdigits(Vecrev(digits(i*j))));
a(n) = my(m = tm(2*n), s=0); forperm([1..2*n], p, s += prod(j=1, n, m[p[2*j-1], p[2*j]]); ); s/(n!*2^n); \\ Michel Marcus, Feb 21 2026

Crossrefs

Cf. A003991, A004086, A391365, A393479 (permanent).

Cf. A354865, A357279, A357420, A357421, A357503, A358158, A358160, A358162, A358164.

Sequence in context: A226339 A157064 A392686 * A058527 A342329 A377135

Adjacent sequences: A393477 A393478 A393479 * A393481 A393482 A393483

Keyword

nonn,base,hard,more

Author

Stefano Spezia, Feb 16 2026

Extensions

a(6)-a(10) from Pontus von Brömssen, Feb 16 2026

a(11) from Sean A. Irvine, Feb 20 2026

Status

approved