A364646 G.f. satisfies A(x) = 1/(1 - 4*x) - x*A(x)^3.

1, 3, 7, 16, 55, 235, 856, 2664, 9055, 37417, 151431, 533452, 1825972, 7141860, 29778280, 113688592, 400940751, 1499506693, 6185139781, 24862774872, 91529003839, 334939413067, 1338383383444, 5510330536000, 21217042841668, 77850045234108, 300471644949940

Offset

0,2

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A364641, A364645, A364647.

Cf. A001700, A349535.

Sequence in context: A143817 A297210 A000963 * A133593 A297154 A305348

Adjacent sequences: A364643 A364644 A364645 * A364647 A364648 A364649

Keyword

nonn

Author

Seiichi Manyama, Jul 31 2023

Status

approved