A391300 Expansion of g^2/(1 + x^3*g^3), where g = 1+x*g^3 is the g.f. of A001764.

1, 2, 7, 29, 138, 703, 3747, 20626, 116351, 669064, 3907442, 23113071, 138186281, 833716631, 5069534022, 31036381679, 191146470099, 1183463411320, 7361847411159, 45988689841012, 288381552451690, 1814602015887109, 11454043053038374, 72507509244304571

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (3*k+2) * binomial(3*n-6*k+2,n-3*k)/(3*n-6*k+2).

Mathematica

Table[ Sum[(-1)^k*(3*k+2)*Binomial[3*n-6*k+2, n-3*k]/(3*n-6*k+2), {k, 0, Floor[n/3]}], {n, 0, 21}] (* Vincenzo Librandi, Dec 07 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*(3*k+2)*binomial(3*n-6*k+2, n-3*k)/(3*n-6*k+2));
(Magma) [&+[(-1)^k*(3*k+2)*Binomial(3*n-6*k+2, n-3*k)/(3*n-6*k+2): k in [0..Floor(n/3)]] : n in [0..30] ]; // Vincenzo Librandi, Dec 07 2025

Crossrefs

Cf. A391296, A391298, A391302.

Cf. A001764, A391127.

Sequence in context: A104252 A391302 A373802 * A018977 A391298 A190736

Adjacent sequences: A391297 A391298 A391299 * A391301 A391302 A391303

Keyword

nonn

Author

Seiichi Manyama, Dec 06 2025

Status

approved