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 A382538 #18 May 17 2025 03:12:10
%S A382538 1,1,15,99,519,3165,19503,115053,688803,4141863,24778355,148376447,
%T A382538 889216143,5326274463,31903872267,191123789739,1144894457103,
%U A382538 6858232252437,41083285178247,246102886383661,1474237118571467,8831178384769525,52901735792001759
%N A382538 Expansion of 1/(1 - x*(1 + 4*x)^(7/2)).
%H A382538 Vincenzo Librandi, <a href="/A382538/b382538.txt">Table of n, a(n) for n = 0..600</a>
%F A382538 a(n) = Sum_{k=0..n} 4^(n-k) * binomial(7*k/2,n-k).
%F A382538 D-finite with recurrence (-n+1)*a(n) +2*(-2*n+11)*a(n-1) +(n-1)*a(n-2) +2*(16*n-25)*a(n-3) +56*(8*n-17)*a(n-4) +224*(16*n-43)*a(n-5) +4480*(4*n-13)*a(n-6) +3584*(16*n-61)*a(n-7) +14336*(8*n-35)*a(n-8) +8192*(16*n-79)*a(n-9) +32768*(2*n-11)*a(n-10)=0. - _R. J. Mathar_, Apr 02 2025
%t A382538 Table[Sum[4^(n-k)* Binomial[7*k/2, n-k],{k,0,n}],{n,0,28}] (* _Vincenzo Librandi_, May 16 2025 *)
%o A382538 (PARI) a(n) = sum(k=0, n, 4^(n-k)*binomial(7*k/2, n-k));
%o A382538 (Magma) R<x>:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(7/2)))); // _Vincenzo Librandi_, May 16 2025
%Y A382538 Cf. A362154, A382536, A382537.
%Y A382538 Cf. A002423.
%K A382538 nonn,easy
%O A382538 0,3
%A A382538 _Seiichi Manyama_, Mar 31 2025