A391171 Expansion of (g/(1 - x*g))^2, where g = 1+x*g^3 is the g.f. of A001764.

1, 4, 16, 70, 332, 1674, 8831, 48192, 269918, 1543038, 8967635, 52827050, 314733791, 1893170136, 11481649248, 70131545106, 431053724184, 2664037363148, 16545312113502, 103207657920842, 646340219455295, 4062186164473520, 25613392731699272, 161979716083884732

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

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

Mathematica

Table[Sum[(k+1)*(k+2)*Binomial[3*n-2*k+2, n-k]/(3*n-2*k+2), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 04 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (k+1)*(k+2)*binomial(3*n-2*k+2, n-k)/(3*n-2*k+2));
(Magma) [&+[(k+1)*(k+2)*Binomial(3*n-2*k+2, n-k)/(3*n-2*k+2): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 04 2025

Crossrefs

Cf. A006013, A390719, A391172, A391173.

Cf. A098746, A391175, A391177.

Cf. A391168, A391174.

Cf. A001764, A374835.

Sequence in context: A394949 A151244 A280767 * A091354 A326654 A246014

Adjacent sequences: A391168 A391169 A391170 * A391172 A391173 A391174

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2025

Status

approved