A367027 G.f. A(x) satisfies A(x) = 1 + x*A(x)^3 - x^2*A(x)^5.

1, 1, 2, 4, 5, -13, -147, -816, -3534, -12650, -35420, -53040, 199056, 2391340, 14555740, 68264112, 261045693, 769660569, 1167906402, -5145668100, -61758940705, -385813067255, -1857144860445, -7266981925560, -21793022441775, -32643056947527, 161919845140752

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

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

G.f.: ( (1/x) * Series_Reversion( x * (1-x+x^2)^2 ) )^(1/2). - Seiichi Manyama, Mar 08 2025

Prog

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

Crossrefs

Cf. A000108, A137265, A200753, A200755.

Cf. A361245, A368969.

Sequence in context: A232207 A136563 A127077 * A104549 A174513 A000063

Adjacent sequences: A367024 A367025 A367026 * A367028 A367029 A367030

Keyword

sign,changed

Author

Seiichi Manyama, Nov 02 2023

Status

approved