A391168 Expansion of g/(1 - x*g)^2, where g = 1+x*g^3 is the g.f. of A001764.

1, 3, 10, 39, 172, 827, 4223, 22513, 123906, 698800, 4017611, 23459981, 138753411, 829497070, 5004289494, 30428025015, 186279229008, 1147233165477, 7102899516394, 44184059607680, 276013127801339, 1730802569428854, 10890903201239142, 68745550922693495

Offset

0,2

Links

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

Formula

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

Mathematica

Table[Sum[(k+1)^2*Binomial[3*n-2*k+1, n-k]/(3*n-2*k+1), {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Dec 03 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, (k+1)^2*binomial(3*n-2*k+1, n-k)/(3*n-2*k+1));
(Magma) [&+[(k+1)^2 * Binomial(3*n-2*k+1, n-k)/(3*n-2*k+1): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 03 2025

Crossrefs

Cf. A001764, A098746, A391169, A391170.

Cf. A391173.

Sequence in context: A221585 A083862 A205543 * A137590 A352174 A124532

Adjacent sequences: A391165 A391166 A391167 * A391169 A391170 A391171

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2025

Status

approved