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 A374488 #30 Aug 25 2025 05:14:30
%S A374488 1,3,24,100,555,2541,12628,59004,281655,1315765,6171132,28692456,
%T A374488 133315273,616780815,2848833120,13124483344,60364983987,277142478921,
%U A374488 1270586298520,5817063737100,26600252408961,121501917998263,554429553154044,2527595449990500
%N A374488 Expansion of 1/(1 - 2*x - 11*x^2)^(3/2).
%H A374488 Paolo Xausa, <a href="/A374488/b374488.txt">Table of n, a(n) for n = 0..1000</a>
%F A374488 a(0) = 1, a(1) = 3; a(n) = ((2*n+1)*a(n-1) + 11*(n+1)*a(n-2))/n.
%F A374488 a(n) = binomial(n+2,2) * A025237(n).
%F A374488 From _Seiichi Manyama_, Aug 20 2025: (Start)
%F A374488 a(n) = ((n+2)/2) * Sum_{k=0..floor(n/2)} 3^k * binomial(n+1,n-2*k) * binomial(2*k+1,k).
%F A374488 a(n) = Sum_{k=0..n} (1/2)^k * (11/2)^(n-k) * (2*k+1) * binomial(2*k,k) * binomial(k,n-k). (End)
%F A374488 a(n) ~ sqrt(n) * (1 + 2*sqrt(3))^(n + 3/2) / (4 * 3^(3/4) * sqrt(Pi)). - _Vaclav Kotesovec_, Aug 21 2025
%t A374488 Module[{x}, CoefficientList[Series[1/(1 - (11*x + 2)*x)^(3/2), {x, 0, 25}], x]] (* _Paolo Xausa_, Aug 25 2025 *)
%o A374488 (PARI) a(n) = binomial(n+2, 2)*sum(k=0, n\2, 3^k*binomial(n, 2*k)*binomial(2*k, k)/(k+1));
%Y A374488 Cf. A102839, A102840, A374487.
%Y A374488 Cf. A014432, A025237, A084603.
%K A374488 nonn,changed
%O A374488 0,2
%A A374488 _Seiichi Manyama_, Jul 09 2024