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 A387284 #17 Aug 26 2025 14:22:14
%S A387284 1,35,714,11130,147126,1739430,18977574,194933310,1910889981,
%T A387284 18049106075,165420791536,1478846110560,12948121954404,
%U A387284 111381159472380,943685046652536,7890986412386280,65229211294855839,533768263527907485,4328710275989203566,34823868658927020750
%N A387284 Expansion of 1/((1-3*x) * (1-7*x))^(7/2).
%H A387284 Vincenzo Librandi, <a href="/A387284/b387284.txt">Table of n, a(n) for n = 0..600</a>
%F A387284 n*a(n) = (10*n+25)*a(n-1) - 21*(n+5)*a(n-2) for n > 1.
%F A387284 a(n) = (-1)^n * Sum_{k=0..n} 7^k * 3^(n-k) * binomial(-7/2,k) * binomial(-7/2,n-k).
%F A387284 a(n) = Sum_{k=0..n} (-4)^k * 3^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).
%F A387284 a(n) = Sum_{k=0..n} 4^k * 7^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).
%F A387284 a(n) = (binomial(n+6,3)/20) * A387276(n).
%F A387284 a(n) = (-1)^n * Sum_{k=0..n} 10^k * (21/10)^(n-k) * binomial(-7/2,k) * binomial(k,n-k).
%t A387284 CoefficientList[Series[1/((1-3x)*(1-7*x))^(7/2),{x,0,33}],x] (* _Vincenzo Librandi_, Aug 26 2025 *)
%o A387284 (PARI) my(N=20, x='x+O('x^N)); Vec(1/((1-3*x)*(1-7*x))^(7/2))
%o A387284 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/((1-3*x) * (1-7*x))^(7/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 26 2025
%Y A387284 Cf. A387238, A387276.
%K A387284 nonn,new
%O A387284 0,2
%A A387284 _Seiichi Manyama_, Aug 24 2025