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A391208

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

1, 0, 1, 6, 34, 194, 1123, 6592, 39170, 235194, 1424887, 8699126, 53464948, 330519704, 2053805908, 12820480400, 80356471098, 505510116138, 3190641381871, 20199154933138, 128227412500634, 816057912305362, 5205538240069691, 33276472563981688, 213141031578036344

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OFFSET

0,4

LINKS

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

FORMULA

G.f.: 1/(1 - x^2*g^6), where g = 1+x*g^3 is the g.f. of A001764.

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

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

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

MATHEMATICA

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