A391173 Expansion of g^2/(1 - x*g)^4, where g = 1+x*g^3 is the g.f. of A001764.

1, 6, 29, 138, 678, 3466, 18369, 100320, 561440, 3205178, 18598797, 109395610, 650819223, 3909560406, 23681726775, 144490912866, 887196759546, 5478092897720, 33993786367640, 211886416196202, 1326009590657203, 8328450802410150, 52482241998624411

Offset

0,2

Links

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

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A391168.

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

Mathematica

Table[Sum[(k+2)*Binomial[k+3, 3]*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+2)*binomial(k+3, 3)*binomial(3*n-2*k+2, n-k)/(3*n-2*k+2));
(Magma) [&+[(k+2)*Binomial(k+3, 3)*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, A391171, A391172.

Cf. A001764, A391168.

Sequence in context: A289801 A359920 A110311 * A030221 A391516 A271753

Adjacent sequences: A391170 A391171 A391172 * A391174 A391175 A391176

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2025

Status

approved