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 A387280 #21 Aug 25 2025 09:21:47
%S A387280 1,20,250,2520,22470,185304,1448580,10895280,79603590,568642360,
%T A387280 3989693708,27585223120,188421602460,1273887926640,8537435428680,
%U A387280 56785445628768,375214194393030,2464893754074360,16109413813808700,104800627073105040,678975482198143284,4382524104695787600
%N A387280 Expansion of 1/((1-2*x) * (1-6*x))^(5/2).
%H A387280 Paolo Xausa, <a href="/A387280/b387280.txt">Table of n, a(n) for n = 0..1000</a>
%F A387280 n*a(n) = (8*n+12)*a(n-1) - 12*(n+3)*a(n-2) for n > 1.
%F A387280 a(n) = (-2)^n * Sum_{k=0..n} 3^k * binomial(-5/2,k) * binomial(-5/2,n-k).
%F A387280 a(n) = 2^n * Sum_{k=0..n} (-2)^k * binomial(-5/2,k) * binomial(n+4,n-k).
%F A387280 a(n) = Sum_{k=0..n} 4^k * 6^(n-k) * binomial(-5/2,k) * binomial(n+4,n-k).
%F A387280 a(n) = (binomial(n+4,2)/6) * A387272(n).
%F A387280 a(n) = (-1)^n * Sum_{k=0..n} 8^k * (3/2)^(n-k) * binomial(-5/2,k) * binomial(k,n-k).
%t A387280 Module[{x}, CoefficientList[Series[1/((3*x - 2)*4*x + 1)^(5/2), {x, 0, 25}], x]] (* _Paolo Xausa_, Aug 25 2025 *)
%o A387280 (PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-2*x)*(1-6*x))^(5/2))
%Y A387280 Cf. A387237, A387272.
%K A387280 nonn,new
%O A387280 0,2
%A A387280 _Seiichi Manyama_, Aug 24 2025