|
%I #11 Jul 20 2022 15:59:37
%S 0,4,28,128,480,1600,4928,14336,39936,107520,281600,720896,1810432,
%T 4472832,10895360,26214400,62390272,147062784,343670784,796917760,
%U 1835008000,4198498304,9550430208,21609054208,48653926400,109051904000,243403849728,541165879296
%N Binomial transform of the sum of the first n even squares (A002492).
%C The inverse binomial transform of a(n) is A002492(n) = 2n(n+1)(2n+1)/3.
%F Conjecture: a(n) = (2^(n-1)*n*(5+6*n+n^2))/3. G.f.: -4*x*(x-1) / (2*x-1)^4. - _Colin Barker_, Apr 06 2014
%F a(n) = (-1)^n * Sum_{k=0..floor(n/2)} binomial(n-k, k) * (-4)^(n-k) * (n-k). - _Joseph M. Shunia_, Jul 20 2022
%t Table[Sum[2 Binomial[n, k] k (k + 1) (2 k + 1)/3, {k, 0, n}], {n, 0, 30}]
%Y Cf. A002492.
%K nonn
%O 0,2
%A _Wesley Ivan Hurt_, Apr 04 2014
|
