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 A387316 #17 Aug 28 2025 11:44:28
%S A387316 1,49,1498,36750,792246,15681666,292137846,5201141946,89399571261,
%T A387316 1494080348761,24403114463728,391038174645664,6165638429715492,
%U A387316 95880046644705876,1473241291627666488,22401020288076984120,337479336374849120991,5042656883996693680719
%N A387316 Expansion of 1/((1-x) * (1-13*x))^(7/2).
%H A387316 Vincenzo Librandi, <a href="/A387316/b387316.txt">Table of n, a(n) for n = 0..800</a>
%F A387316 n*a(n) = (14*n+35)*a(n-1) - 13*(n+5)*a(n-2) for n > 1.
%F A387316 a(n) = (-1)^n * Sum_{k=0..n} 13^k * binomial(-7/2,k) * binomial(-7/2,n-k).
%F A387316 a(n) = Sum_{k=0..n} (-12)^k * binomial(-7/2,k) * binomial(n+6,n-k).
%F A387316 a(n) = Sum_{k=0..n} 12^k * 13^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).
%F A387316 a(n) = (binomial(n+6,3)/20) * A387311(n).
%F A387316 a(n) = (-1)^n * Sum_{k=0..n} 14^k * (13/14)^(n-k) * binomial(-7/2,k) * binomial(k,n-k).
%t A387316 CoefficientList[Series[1/((1-x)*(1-13*x))^(7/2),{x,0,33}],x] (* _Vincenzo Librandi_, Aug 28 2025 *)
%o A387316 (PARI) my(N=20, x='x+O('x^N)); Vec(1/((1-x)*(1-13*x))^(7/2))
%o A387316 (Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/((1-x) * (1-13*x))^(7/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // _Vincenzo Librandi_, Aug 28 2025
%Y A387316 Cf. A385716, A387315.
%K A387316 nonn,new
%O A387316 0,2
%A A387316 _Seiichi Manyama_, Aug 25 2025