A391178 Expansion of g^3/(1 - x*g), where g = 1+x*g^3 is the g.f. of A001764.

1, 4, 17, 79, 393, 2054, 11133, 62032, 353168, 2045691, 12017773, 71434015, 428836918, 2596356079, 15835256409, 97201308135, 600031757391, 3722682711953, 23199885340932, 145166722386319, 911656880093062, 5744254686792063, 36303441154228601, 230071865210018678

Offset

0,2

Links

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

Formula

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

a(n) = A098746(n+2) - A098746(n+1).

Mathematica

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

Prog

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

Crossrefs

Cf. A001764, A391174, A391175, A391176.

Cf. A098746, A390719.

Sequence in context: A364030 A053486 A151249 * A289924 A218134 A110307

Adjacent sequences: A391175 A391176 A391177 * A391179 A391180 A391181

Keyword

nonn,changed

Author

Seiichi Manyama, Dec 01 2025

Status

approved