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 A367548 #15 Jul 30 2025 09:45:15
%S A367548 1,1,3,-2,19,-54,222,-804,3075,-11630,44458,-170268,654766,-2524508,
%T A367548 9758556,-37802952,146724579,-570450078,2221230066,-8660901612,
%U A367548 33811886394,-132148736148,517012584036,-2024632609272,7935337877454,-31126450260204,122183595168612
%N A367548 a(n) = Sum_{k = 0..n} binomial(-n, k) * 2^(n - k).
%F A367548 a(n) = 4^n*3^(-n) - binomial(-n, n+1) * hypergeom([1, 2*n+1], [n + 2], -1/2) / 2.
%F A367548 a(n) = [x^n] (3 + 12*x + sqrt(4*x + 1)*(4*x + 3))/(6 + 16*x - 32*x^2).
%F A367548 D-finite with recurrence 9*n*a(n) +6*(6*n-7)*a(n-1) +16*(-n-4)*a(n-2) +32*(-2*n+5)*a(n-3)=0. - _R. J. Mathar_, Jan 11 2024
%F A367548 From _Seiichi Manyama_, Jul 30 2025: (Start)
%F A367548 a(n) = [x^n] 1/((1-2*x) * (1+x)^n).
%F A367548 a(n) = Sum_{k=0..n} (-1)^k * 3^(n-k) * binomial(2*n,k). (End)
%p A367548 seq(add(binomial(-n, k)*2^(n - k), k = 0..n), n = 0..26);
%t A367548 Table[Sum[Binomial[-n,k]2^(n-k),{k,0,n}],{n,0,30}] (* _Harvey P. Dale_, Apr 03 2024 *)
%Y A367548 Cf. A032443.
%K A367548 sign
%O A367548 0,3
%A A367548 _Peter Luschny_, Nov 29 2023