A371537 - OEIS

%I #9 Mar 27 2024 08:48:51

%S 1,2,11,90,845,8620,92792,1037474,11930952,140223730,1676824810,

%T 20336742860,249554057158,3092735367966,38653949888993,

%U 486656046354650,6166315484899445,78573243500307870,1006223574171080479,12943581721362983708,167170200918998754129

%N G.f. A(x) satisfies A(x) = (1 + x*A(x)^3 / (1+x))^2.

%F a(n) = 2 * Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+2,k)/(6*k+2).

%F G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A349362.

%o (PARI) a(n) = 2*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+2, k)/(6*k+2));

%Y Cf. A349362, A371538, A371539, A371540, A371541.

%Y Cf. A371523.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 26 2024