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 A082145 #32 Jan 16 2024 01:38:35
%S A082145 1,5,42,336,2640,20592,160160,1244672,9674496,75246080,585761792,
%T A082145 4564377600,35602145280,277970595840,2172375244800,16992801914880,
%U A082145 133035751833600,1042374243778560,8173537721057280,64136851016908800,503613708419727360,3956964851869286400
%N A082145 A subdiagonal of number array A082137.
%H A082145 G. C. Greubel, <a href="/A082145/b082145.txt">Table of n, a(n) for n = 0..1000</a>
%F A082145 a(n) = ( 2^(n-1) + (0^n)/2 )*binomial(2*n+3, n).
%F A082145 (n+3)*a(n) +2*(-7*n-13)*a(n-1) +24*(2*n+1)*a(n-2)=0. - _R. J. Mathar_, Oct 29 2014
%F A082145 From _Amiram Eldar_, Jan 16 2024: (Start)
%F A082145 Sum_{n>=0} 1/a(n) = 37/7 - 208*arcsin(1/(2*sqrt(2)))/(7*sqrt(7)).
%F A082145 Sum_{n>=0} (-1)^n/a(n) = 296*log(2)/27 - 61/9. (End)
%e A082145 a(0) = ( 2^(-1)+(0^0)/2 )*C(3,0) = ( 1/2+1/2 )*1 = 1 (use 0^0 = 1). - clarified by _Jon Perry_, Oct 29 2014
%p A082145 Z:=(1-3*z-sqrt(1-4*z))/sqrt(1-4*z)/64: Zser:=series(Z, z=0, 32): seq(coeff(Zser*2^(n+1), z, n), n=4..23); # _Zerinvary Lajos_, Jan 01 2007
%t A082145 Join[{1}, Table[2^(n-1)* Binomial[2*n+3,n], {n,1,30}]] (* _G. C. Greubel_, Feb 05 2018 *)
%o A082145 (Magma) [(2^(n-1)+(0^n)/2)*Binomial(2*n+3, n): n in [0..30]]; // _Vincenzo Librandi_, Oct 30 2014
%o A082145 (PARI) for(n=0,30, print1((2^(n-1) + 0^n/2)*Binomial(2*n+3,n), ", ")) \\ _G. C. Greubel_, Feb 05 2018
%Y A082145 Cf. A069723, A082143, A082144.
%K A082145 nonn,easy
%O A082145 0,2
%A A082145 _Paul Barry_, Apr 06 2003