A164583 - OEIS

%I #9 May 10 2024 11:09:29

%S 1,36,400,3136,20736,123904,692224,3686400,18939904,94633984,

%T 462422016,2218786816,10485760000,48922361856,225754218496,

%U 1031865892864,4677219385344,21045339750400,94076963651584,418089296461824

%N a(n) = 4^n*(2n + 1)^2.

%C The aerated signed sequence 0,-1,0,36,0,-400,... with general term -(-4)^((n-1)/2)*n^2*(1-(-1)^n)/2

%C is the Hankel transform of the aeration 0,1,0,6,0,30,0,140,... of A002457.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-48,64).

%F G.f.: (1+24x+16x^2)/(1-4x)^3.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Aug 17 2009