A391405 - OEIS

%I #7 Dec 09 2025 08:17:19

%S 1,1,7,30,153,805,4397,24647,141020,820201,4835029,28823700,173471074,

%T 1052554765,6431805843,39546649026,244489418103,1518872793184,

%U 9477032121080,59364204189857,373178685365818,2353473823288829,14886098712983627,94411553259696275

%N Expansion of g^3/(1 + x*g)^2, where g = 1+x*g^3 is the g.f. of A001764.

%F a(n) = Sum_{k=0..n} (-1)^k * (k+1) * (k+3) * binomial(3*n-2*k+3,n-k)/(3*n-2*k+3).

%o (PARI) a(n) = sum(k=0, n, (-1)^k*(k+1)*(k+3)*binomial(3*n-2*k+3, n-k)/(3*n-2*k+3));

%Y Cf. A374836, A391404.

%Y Cf. A001764, A389115, A391174.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 08 2025