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%I #17 Jan 24 2022 15:58:46
%S 1,19,51,201,723,2709,10161,38459,146297,559135,2145021,8255579,
%T 31861021,123256499,477823891,1855782329,7219352971,28125910829,
%U 109720617991,428537256449,1675561707271,6557869020329,25689734662771,100720871774981,395197661173123
%N a(n) = A054108(n) + 4*(-1)^n.
%F a(n) = C(2(n+1),n+1) - a(n-1) with a(1) = 1. - _Chai Wah Wu_, Jan 19 2022
%t s[0] = 1; s[n_] := Binomial[2 n + 2, n + 1] - s[n - 1];
%t Table[s[n], {n, 0, 10}]; (* A054108 *)
%t a[n_] := s[n] + 4*(-1)^n;
%t Table[a[n], {n, 1, 30}] (* A349554 *)
%o (Python)
%o from math import comb
%o def A349554(n): return (1 if n % 2 else -1)*(sum((-1 if k % 2 else 1)*comb(2*k,k) for k in range(n+2))-4) # _Chai Wah Wu_, Jan 19 2022
%o (PARI) a(n) = (-1)^(n+1)*sum(k=0,n+1,(-1)^k*binomial(2*k,k)) + 4*(-1)^n; \\ _Michel Marcus_, Jan 19 2022
%Y Cf. A000984, A054108.
%K nonn
%O 1,2
%A _Clark Kimberling_, Dec 30 2021
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