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 A387281 #16 Aug 25 2025 09:25:01
%S A387281 1,28,462,5880,63966,626472,5692764,48919728,402648246,3202791592,
%T A387281 24780247492,187393703952,1390208264172,10146829592592,73029572999352,
%U A387281 519260074512480,3652939914500646,25457292175929768,175932472247239092,1206772898939860560,8221969006750158660
%N A387281 Expansion of 1/((1-2*x) * (1-6*x))^(7/2).
%H A387281 Paolo Xausa, <a href="/A387281/b387281.txt">Table of n, a(n) for n = 0..1000</a>
%F A387281 n*a(n) = (8*n+20)*a(n-1) - 12*(n+5)*a(n-2) for n > 1.
%F A387281 a(n) = (-2)^n * Sum_{k=0..n} 3^k * binomial(-7/2,k) * binomial(-7/2,n-k).
%F A387281 a(n) = 2^n * Sum_{k=0..n} (-2)^k * binomial(-7/2,k) * binomial(n+6,n-k).
%F A387281 a(n) = Sum_{k=0..n} 4^k * 6^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).
%F A387281 a(n) = (binomial(n+6,3)/20) * A387273(n).
%F A387281 a(n) = (-1)^n * Sum_{k=0..n} 8^k * (3/2)^(n-k) * binomial(-7/2,k) * binomial(k,n-k).
%t A387281 Module[{x}, CoefficientList[Series[1/((3*x - 2)*4*x + 1)^(7/2), {x, 0, 25}], x]] (* _Paolo Xausa_, Aug 25 2025 *)
%o A387281 (PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-2*x)*(1-6*x))^(7/2))
%Y A387281 Cf. A387273.
%K A387281 nonn,new
%O A387281 0,2
%A A387281 _Seiichi Manyama_, Aug 24 2025