%I #16 Sep 08 2022 08:44:51
%S 1,8,50,248,1048,3952,13696,44480,137216,406016,1160704,3223552,
%T 8734720,23171072,60342272,154615808,390529024,973864960,2400845824,
%U 5857869824,14159446016,33935065088,80698408960,190534647808,446911479808,1041898668032,2415348678656,5570035712000
%N EXPCONV of squares A000290 with themselves.
%H Vincenzo Librandi, <a href="/A033463/b033463.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,80,-80,32).
%F a(n) = 2^(n-4)*(n^4+6*n^3+19*n^2+22*n+16). E.g.f.: (1+3*x+x^2)^2*exp(2*x). O.g.f.: (1-2*x+10*x^2-12*x^3+8*x^4)/(1-2*x)^5. Recurrence: a(n) = 10*a(n-1)-40*a(n-2)+80*a(n-3)-80*a(n-4)+32*a(n-5). a(n) = Sum_{k=0..n} binomial(n, k)*(k+1)^2*(n-k+1)^2. - _Vladeta Jovovic_, Sep 17 2003
%t LinearRecurrence[{10,-40,80,-80,32},{1,8,50,248,1048},30] (* _Harvey P. Dale_, Aug 26 2014 *)
%t CoefficientList[Series[(1 - 2 x + 10 x^2 - 12 x^3 + 8 x^4)/(1 - 2 x)^5, {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 27 2014 *)
%o (Magma) I:=[1,8,50,248,1048]; [n le 5 select I[n] else 10*Self(n-1)-40*Self(n-2)+80*Self(n-3)-80*Self(n-4)+32*Self(n-5): n in [1..30]]; // _Vincenzo Librandi_, Aug 27 2014
%K nonn
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Aug 27 2014