A360084 a(n) = Sum_{k=0..n} (-1)^k * binomial(3*k,n-k) * Catalan(k).

1, -1, -1, 4, -2, -14, 36, -1, -191, 418, 182, -2904, 5546, 5226, -47466, 78843, 121489, -813060, 1157400, 2659695, -14364997, 17078752, 56866292, -259091498, 246553176, 1202210486, -4736784794, 3346401868, 25255328948, -87323306720, 39123129700

Offset

0,4

Links

Table of n, a(n) for n=0..30.

Formula

G.f. A(x) satisfies A(x) = 1/(1 + x * (1+x)^3 * A(x)).

G.f.: 2 / (1 + sqrt( 1 + 4*x*(1+x)^3 )).

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(3*k, n-k)*binomial(2*k, k)/(k+1));
(PARI) my(N=40, x='x+O('x^N)); Vec(2/(1+sqrt(1+4*x*(1+x)^3)))

Crossrefs

Cf. A360085, A360086.

Cf. A000108.

Sequence in context: A317738 A224893 A087957 * A019061 A019012 A154333

Adjacent sequences: A360081 A360082 A360083 * A360085 A360086 A360087

Keyword

sign

Author

Seiichi Manyama, Jan 25 2023

Status

approved