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A369906 Sum of the permanents of all 2 X 2 submatrices in the n X n Pascal matrix.

%I A369906 #14 Feb 19 2024 09:00:48
%S A369906 0,0,1,9,50,234,1016,4256,17509,71349,289223,1168815,4714425,18991401,
%T A369906 76434373,307411285,1235697666,4964876706,19940653388,80062371380,
%U A369906 321361753426,1289589924226,5173842730758,20753408180790,83231772855896,333749033253560
%N A369906 Sum of the permanents of all 2 X 2 submatrices in the n X n Pascal matrix.
%H A369906 Alois P. Heinz, <a href="/A369906/b369906.txt">Table of n, a(n) for n = 0..1661</a>
%H A369906 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permanent_(mathematics)">Permanent (mathematics)</a>
%F A369906 a(n) ~ 4^n/3 * (1 - 1/sqrt(Pi*n)). - _Vaclav Kotesovec_, Feb 19 2024
%p A369906 a:= proc(n) option remember; `if`(n<5, [0, 0, 1, 9, 50][n+1],
%p A369906       ((13*n-12)*a(n-1)-8*(8*n-15)*a(n-2)+4*(37*n-105)*
%p A369906        a(n-3)-40*(4*n-15)*a(n-4)+32*(2*n-9)*a(n-5))/n)
%p A369906     end:
%p A369906 seq(a(n), n=0..32);
%Y A369906 Column k=2 of A369559.
%Y A369906 Cf. A007318, A306376 (same for determinants).
%K A369906 nonn
%O A369906 0,4
%A A369906 _Alois P. Heinz_, Feb 05 2024