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A330287 Permanent of the n-th principal submatrix M(n) of A319840. 4
1, 1, 8, 208, 11488, 1093056, 158972160, 32734095360, 9049229328384, 3230305304002560, 1445344680438005760, 791762592707031859200, 521023492500173338705920, 405448567547957922512240640, 368210800911998093644372377600, 385879616532879866123928993792000, 462151848929747968377341029122048000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The matrix M(n) is defined as M[i,j,n] = i*j if i < 3 or j < 3 and M[i,j,n] = 2*(i + j) - 4 otherwise.

det(M(0)) = det(M(1)) = 1 and det(M(n)) = 0 for n > 1.

For n > 0, the trace of the matrix M(n) is A001844(n-1).

For n > 0, the antitrace of the matrix M(n) is A005893(n-1).

For n > 1, the super- and subdiagonal sum is A001105(n-1).

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..35

FORMULA

a(n) ~ c * A238261^n * n!^2 / sqrt(n), where c = 0.0286685259829... - Vaclav Kotesovec, Aug 19 2021

EXAMPLE

For n = 1 the matrix M(1) is

  1

with permanent a(1) = 1.

For n = 2 the matrix M(2) is

  1, 2

  2, 4

with permanent a(2) = 8.

For n = 3 the matrix M(3) is

  1,  2,  3

  2,  4,  6

  3,  6,  8

with permanent a(3) = 208.

PROG

(PARI) tm(n) = matrix(n, n, i, j, if ((i<3) || (j<3), i*j, 2*(i+j)-4));

a(n) = matpermanent(tm(n));

CROSSREFS

Cf. A001105, A001844, A005893, A319840.

Sequence in context: A204247 A063856 A090962 * A279663 A294970 A275286

Adjacent sequences:  A330284 A330285 A330286 * A330288 A330289 A330290

KEYWORD

nonn

AUTHOR

Stefano Spezia, Dec 11 2019

STATUS

approved

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Last modified December 2 12:01 EST 2021. Contains 349440 sequences. (Running on oeis4.)