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 A378551 #13 Nov 30 2024 09:49:24
%S A378551 1,2,20,206,2200,24062,267500,3009050,34150000,390265190,4484762500,
%T A378551 51771831146,599921125000,6974108163778,81297715937500,
%U A378551 949957147566086,11123368187500000,130487420114543110,1533247106445312500,18042303960492212810,212590835968046875000
%N A378551 a(n) = Sum_{k=0..n} 4^k * binomial(n/2+k-1,k) * binomial(n-1,n-k).
%F A378551 a(n) = [x^n] 1/(1 - 4*x/(1-x))^(n/2).
%t A378551 a[n_]:=SeriesCoefficient[ 1/(1 - 4*x/(1-x))^(n/2),{x,0,n}]; Array[a,21,0] (* _Stefano Spezia_, Nov 30 2024 *)
%o A378551 (PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2+k-1, k)*binomial(n-1, n-k));
%Y A378551 Cf. A002002, A378552.
%Y A378551 Cf. A372109.
%K A378551 nonn
%O A378551 0,2
%A A378551 _Seiichi Manyama_, Nov 30 2024