This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A082144 #18 Jan 16 2024 01:39:17
%S A082144 1,4,30,224,1680,12672,96096,732160,5601024,42997760,331082752,
%T A082144 2556051456,19778969600,153363087360,1191302553600,9268801044480,
%U A082144 72219408138240,563445537177600,4401135695953920,34414895667609600,269374774271016960,2110381254330286080
%N A082144 A subdiagonal of number array A082137.
%H A082144 G. C. Greubel, <a href="/A082144/b082144.txt">Table of n, a(n) for n = 0..1000</a>
%F A082144 a(n) = (2^(n-1) + 0^n/2)*C(2*n+2, n).
%F A082144 (n+2)*a(n) +12*(-n-1)*a(n-1) +16*(2*n-1)*a(n-2)=0. - _R. J. Mathar_, Oct 29 2014
%F A082144 From _Amiram Eldar_, Jan 16 2024: (Start)
%F A082144 Sum_{n>=0} 1/a(n) = 88*arccot(sqrt(7))/(7*sqrt(7)) - 3/7.
%F A082144 Sum_{n>=0} (-1)^n/a(n) = 52*log(2)/27 - 5/9. (End)
%e A082144 a(0)=(2^(-1)+(0^0)/2)C(2,0)=2*(1/2)=1 (use 0^0=1).
%t A082144 Join[{1}, Table[2^(n-1)*Binomial[2*n+2, n], {n,1,50}]] (* _G. C. Greubel_, Feb 05 2018 *)
%o A082144 (PARI) for(n=0,30, print1((2^(n-1) + 0^n/2)*Binomial(2*n+2,n), ", ")) \\ _G. C. Greubel_, Feb 05 2018
%o A082144 (Magma) [(2^(n-1) + 0^n/2)*Binomial(2*n+2,n): n in [0..30]]; // _G. C. Greubel_, Feb 05 2018
%Y A082144 Cf. A069723, A082137, A082143, A082145.
%K A082144 easy,nonn
%O A082144 0,2
%A A082144 _Paul Barry_, Apr 06 2003