A390719 a(n) = Sum_{k=0..n} (k+2) * binomial(3*n-2*k+2,n-k)/(3*n-2*k+2).

1, 3, 11, 47, 222, 1121, 5930, 32451, 182207, 1043858, 6077706, 35859253, 213932707, 1288352838, 7821620103, 47818928943, 294148895958, 1819231110581, 11305825203878, 70565359982802, 442149898755814, 2780202192726502, 17537754449862543, 110953785399196001, 703842560175324026, 4475911393785764481

Offset

0,2

Links

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

Formula

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

Mathematica

Table[Sum[(k+2)*Binomial[3*n-2*k+2, n-k]/(3*n-2*k+2), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Nov 17 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (k+2)*binomial(3*n-2*k+2, n-k)/(3*n-2*k+2));
(Magma) [&+[(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, Nov 17 2025

Crossrefs

Cf. A000245, A390720, A390721.

Cf. A001764.

Sequence in context: A301409 A295539 A359120 * A174347 A062146 A216947

Adjacent sequences: A390716 A390717 A390718 * A390720 A390721 A390722

Keyword

nonn

Author

Seiichi Manyama, Nov 16 2025

Status

approved