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 A375248 #19 Aug 07 2024 15:12:06
%S A375248 1,6,35,168,756,3192,12936,50688,193479,722722,2651649,9581936,
%T A375248 34176324,120526056,420852204,1456709328,5002984791,17062825626,
%U A375248 57827993685,194871361608,653285629920,2179701604080,7241015510820,23958512912880,78978801164445
%N A375248 Expansion of (1 - x)/(1 - 2*x - 3*x^2)^(7/2).
%F A375248 a(n) = (binomial(n+5,3)/10) * Sum_{k=0..floor(n/2)} binomial(n+2,n-2*k) * binomial(2*k+2,k).
%F A375248 a(n) = (binomial(n+5,3)/10) * A014531(n+1).
%F A375248 a(n) = ((n+5)/(n*(n+4))) * ((2*n+3)*a(n-1) + 3*(n+4)*a(n-2)).
%F A375248 a(n) = (1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*hypergeom([(1-n)/2, -n/2], [3], 4)/120. - _Stefano Spezia_, Aug 07 2024
%t A375248 a[n_]:=(1+n)(2+n)(3+n)(4+n)(5+n)Hypergeometric2F1[(1-n)/2,-n/2,3,4]/120; Array[a,25,0] (* _Stefano Spezia_, Aug 07 2024 *)
%o A375248 (PARI) my(N=30, x='x+O('x^N)); Vec((1-x)/(1-2*x-3*x^2)^(7/2))
%Y A375248 First differences of A374506.
%Y A375248 Cf. A046717, A109188, A371408.
%Y A375248 Cf. A014531, A375253.
%K A375248 nonn
%O A375248 0,2
%A A375248 _Seiichi Manyama_, Aug 07 2024