A391405 Expansion of g^3/(1 + x*g)^2, where g = 1+x*g^3 is the g.f. of A001764.

1, 1, 7, 30, 153, 805, 4397, 24647, 141020, 820201, 4835029, 28823700, 173471074, 1052554765, 6431805843, 39546649026, 244489418103, 1518872793184, 9477032121080, 59364204189857, 373178685365818, 2353473823288829, 14886098712983627, 94411553259696275

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

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).

Prog

(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));

Crossrefs

Cf. A374836, A391404.

Cf. A001764, A389115, A391174.

Sequence in context: A180786 A343755 A026653 * A271554 A296013 A196338

Adjacent sequences: A391402 A391403 A391404 * A391406 A391407 A391408

Keyword

nonn

Author

Seiichi Manyama, Dec 08 2025

Status

approved