A391060 - OEIS

A391060

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

1, 1, 4, 15, 68, 333, 1727, 9317, 51758, 294068, 1700827, 9980653, 59274015, 355592894, 2151707068, 13117292347, 80486635016, 496688096931, 3080658090710, 19194089036648, 120075994871807, 753943787632022, 4749729156662452, 30013614335452595, 190184864457166325, 1208214303761406925

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

FORMULA

a(n) = Sum_{k=0..floor(n/2)} (2*k+1) * binomial(3*n-4*k+1,n-2*k)/(3*n-4*k+1).

MATHEMATICA

Table[Sum[(2*k+1)*Binomial[3*n-4*k+1, n-2*k]/(3*n-4*k+1), {k, 0, Floor[n/2]}], {n, 0, 25}] (* Vincenzo Librandi, Dec 01 2025 *)

PROG

(PARI) a(n) = sum(k=0, n\2, (2*k+1)*binomial(3*n-4*k+1, n-2*k)/(3*n-4*k+1));

(Magma) [&+[(2*k+1)*Binomial(3*n-4*k+1, n-2*k)/(3*n-4*k+1): k in [0..Floor(n/2)]] : n in [0..40] ]; // Vincenzo Librandi, Dec 01 2025