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).

1, 12, 2448, 2900160, 3335369728, 16355507060736, 202873109257748480, 5520786912662854893568, 304515605038514679874846720, 31568014831906551177163996921856, 5785425274398818300907155436515360768, 1783302045417843100606023721285336961122304, 886715046570481808433485979311322483302619676672

Offset

0,2

Links

Table of n, a(n) for n=0..12.

G. E. Andrews, W. Gawronski, and L. L. Littlejohn, The Legendre-Stirling Numbers, Discrete Mathematics, Volume 311, Issue 14, 28 July 2011, Pages 1255-1272.

Mathematica

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]

Crossrefs

Cf. A069135 (determinant), A071951.

Sequence in context: A135398 A203426 A268589 * A228289 A306391 A195536

Adjacent sequences: A372340 A372341 A372342 * A372344 A372345 A372346

Keyword

nonn

Author

Stefano Spezia, Apr 28 2024

Status

approved