Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Nov 30 2024 09:49:24
%S 1,2,20,206,2200,24062,267500,3009050,34150000,390265190,4484762500,
%T 51771831146,599921125000,6974108163778,81297715937500,
%U 949957147566086,11123368187500000,130487420114543110,1533247106445312500,18042303960492212810,212590835968046875000
%N a(n) = Sum_{k=0..n} 4^k * binomial(n/2+k-1,k) * binomial(n-1,n-k).
%F a(n) = [x^n] 1/(1 - 4*x/(1-x))^(n/2).
%t a[n_]:=SeriesCoefficient[ 1/(1 - 4*x/(1-x))^(n/2),{x,0,n}]; Array[a,21,0] (* _Stefano Spezia_, Nov 30 2024 *)
%o (PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2+k-1, k)*binomial(n-1, n-k));
%Y Cf. A002002, A378552.
%Y Cf. A372109.
%K nonn,new
%O 0,2
%A _Seiichi Manyama_, Nov 30 2024