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 A387343 #20 Aug 28 2025 11:44:39
%S A387343 1,20,270,3080,31990,312984,2937900,26751120,237977190,2078447800,
%T A387343 17884238372,152002796400,1278603975740,10660760170480,88213513627800,
%U A387343 725107271106336,5925674432448390,48175954959638520,389871795632108020,3142078444590396080,25228464363569709396
%N A387343 Expansion of 1/(1 - 8*x + 4*x^2)^(5/2).
%H A387343 Vincenzo Librandi, <a href="/A387343/b387343.txt">Table of n, a(n) for n = 0..800</a>
%F A387343 n*a(n) = 4*(2*n+3)*a(n-1) - 4*(n+3)*a(n-2) for n > 1.
%F A387343 a(n) = (binomial(n+4,2)/6) * A387339(n).
%F A387343 a(n) = (-1)^n * Sum_{k=0..n} (1/2)^(n-4*k) * binomial(-5/2,k) * binomial(k,n-k).
%t A387343 CoefficientList[Series[1/(1-8*x+4*x^2)^(5/2),{x,0,33}],x] (* _Vincenzo Librandi_, Aug 28 2025 *)
%o A387343 (PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-8*x+4*x^2)^(5/2))
%o A387343 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/(1 - 8*x + 4*x^2)^(5/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 28 2025
%Y A387343 Cf. A069835, A331515, A387344.
%Y A387343 Cf. A002802, A387313, A387341.
%Y A387343 Cf. A387339.
%K A387343 nonn,new
%O A387343 0,2
%A A387343 _Seiichi Manyama_, Aug 27 2025