A371494 - OEIS

%I #8 Mar 25 2024 09:21:35

%S 1,2,5,18,72,310,1399,6532,31287,152876,759034,3818410,19420713,

%T 99697784,515909606,2688267462,14093211259,74281217492,393389969722,

%U 2092312452404,11171325560120,59854910468196,321717833732186,1734250394445622,9373581927760595

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

%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(3*k+1,k)/(k+1).

%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(3*k+1, k)/(k+1));

%Y Cf. A001006, A371495, A371496.

%Y Cf. A006013.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 25 2024