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 A387314 #13 Aug 28 2025 11:59:05
%S A387314 1,35,756,13020,196266,2709630,35148036,435203340,5198003811,
%T A387314 60326090825,683903083864,7603632658440,83157463636884,
%U A387314 896739874849980,9553010933452824,100690915725416520,1051393771423717029,10887352006705432335,111903813927216900204,1142507997942276850500
%N A387314 Expansion of 1/((1-x) * (1-9*x))^(7/2).
%H A387314 Vincenzo Librandi, <a href="/A387314/b387314.txt">Table of n, a(n) for n = 0..800</a>
%F A387314 n*a(n) = (10*n+25)*a(n-1) - 9*(n+5)*a(n-2) for n > 1.
%F A387314 a(n) = (-1)^n * Sum_{k=0..n} 9^k * binomial(-7/2,k) * binomial(-7/2,n-k).
%F A387314 a(n) = Sum_{k=0..n} (-8)^k * binomial(-7/2,k) * binomial(n+6,n-k).
%F A387314 a(n) = Sum_{k=0..n} 8^k * 9^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).
%F A387314 a(n) = (binomial(n+6,3)/20) * A387308(n).
%F A387314 a(n) = (-1)^n * Sum_{k=0..n} 10^k * (9/10)^(n-k) * binomial(-7/2,k) * binomial(k,n-k).
%t A387314 CoefficientList[Series[1/((1-x)*(1-9*x))^(7/2),{x,0,33}],x] (* _Vincenzo Librandi_, Aug 28 2025 *)
%o A387314 (PARI) my(N=20, x='x+O('x^N)); Vec(1/((1-x)*(1-9*x))^(7/2))
%o A387314 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/((1-x) * (1-9*x))^(7/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 28 2025
%Y A387314 Cf. A387308.
%K A387314 nonn,new
%O A387314 0,2
%A A387314 _Seiichi Manyama_, Aug 25 2025