A381784 - OEIS

%I #7 Mar 07 2025 10:47:20

%S 1,2,15,153,1799,22969,309479,4331175,62349575,917335467,13732751589,

%T 208509835114,3203279694575,49701110565986,777708690091907,

%U 12258870836704797,194475105262057575,3102607480658510165,49746656826517452788,801205735002960886531,12956005807148939155717

%N G.f. A(x) satisfies A(x) = (1 + x*A(x)^4) * C(x*A(x)^2), where C(x) is the g.f. of A000108.

%F a(n) = (1/(4*n+1)) * Sum_{k=0..n} binomial(4*n+1,k) * binomial(4*n-2*k+1,n-k).

%o (PARI) a(n) = sum(k=0, n, binomial(4*n+1, k)*binomial(4*n-2*k+1, n-k))/(4*n+1);

%Y Cf. A234461, A381774.

%Y Cf. A000108.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 07 2025