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A306376 Sum of the 2 X 2 minors in the n X n Pascal matrix.

%I A306376 #17 Feb 19 2024 09:05:07
%S A306376 0,0,1,7,34,144,574,2226,8533,32587,124453,476145,1826175,7022379,
%T A306376 27072487,104614863,405122290,1571859864,6109296442,23781666198,
%U A306376 92704406320,361832294964,1413879679672,5530590849168,21654384302110,84859670743770,332818903663390
%N A306376 Sum of the 2 X 2 minors in the n X n Pascal matrix.
%H A306376 Alois P. Heinz, <a href="/A306376/b306376.txt">Table of n, a(n) for n = 0..1664</a>
%H A306376 Wikipedia, <a href="https://en.wikipedia.org/wiki/Minor_(linear_algebra)">Minor (linear algebra)</a>
%F A306376 G.f.: -1/(2*(x-1))*(1/(2*x-1)+1/sqrt(1-4*x)).
%F A306376 a(n) ~ 2^(2*n+1) / (3*sqrt(Pi*n)). - _Vaclav Kotesovec_, Feb 19 2024
%p A306376 a:= proc(n) option remember; `if`(n<3, (n-1)*n/2,
%p A306376      ((7*n^2-16*n+6)*a(n-1)-2*(7*n^2-17*n+9)*a(n-2)+
%p A306376       4*(n-1)*(2*n-3)*a(n-3))/(n*(n-2)))
%p A306376     end:
%p A306376 seq(a(n), n=0..30);
%t A306376 a[n_] := a[n] = If[n < 3, (n-1)n/2,
%t A306376      ((7n^2 - 16n + 6) a[n-1] - 2(7n^2 - 17n + 9) a[n-2] +
%t A306376      4(n-1)(2n-3) a[n-3])/(n(n-2))];
%t A306376 a /@ Range[0, 30] (* _Jean-François Alcover_, May 03 2021, after _Alois P. Heinz_ *)
%Y A306376 Column k=2 of A184173.
%Y A306376 Cf. A007318, A369906.
%K A306376 nonn
%O A306376 0,4
%A A306376 _Alois P. Heinz_, Feb 11 2019