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 A387238 #21 Aug 24 2025 11:34:30
%S A387238 1,21,266,2646,22806,178794,1310694,9140274,61330269,399107709,
%T A387238 2533330800,15751925280,96257031780,579556206180,3445117599480,
%U A387238 20252115155160,117890464642335,680320688005035,3895668955041710,22152779612619810,125183331416173030
%N A387238 Expansion of 1/((1-x) * (1-5*x))^(7/2).
%H A387238 Vincenzo Librandi, <a href="/A387238/b387238.txt">Table of n, a(n) for n = 0..500</a>
%F A387238 n*a(n) = (6*n+15)*a(n-1) - 5*(n+5)*a(n-2) for n > 1.
%F A387238 a(n) = (-1)^n * Sum_{k=0..n} 5^k * binomial(-7/2,k) * binomial(-7/2,n-k).
%F A387238 a(n) = Sum_{k=0..n} (-4)^k * binomial(-7/2,k) * binomial(n+6,n-k).
%F A387238 a(n) = Sum_{k=0..n} 4^k * 5^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).
%F A387238 a(n) = (binomial(n+6,3)/20) * A387239(n).
%F A387238 a(n) = (-1)^n * Sum_{k=0..n} 6^k * (5/6)^(n-k) * binomial(-7/2,k) * binomial(k,n-k).
%t A387238 CoefficientList[Series[1/((1-x)*(1-5*x))^(7/2),{x,0,33}],x] (* _Vincenzo Librandi_, Aug 24 2025 *)
%o A387238 (PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-x)*(1-5*x))^(7/2))
%o A387238 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/((1-x) * (1-5*x))^(7/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 24 2025
%Y A387238 Cf. A026375, A385563, A387237.
%Y A387238 Cf. A126190, A374509, A387239.
%K A387238 nonn,new
%O A387238 0,2
%A A387238 _Seiichi Manyama_, Aug 23 2025