A367045 G.f. satisfies A(x) = 1 - x^2 + x*A(x)^4.

1, 1, 3, 18, 112, 755, 5348, 39302, 296916, 2291861, 17997052, 143319918, 1154728056, 9395809374, 77099733884, 637298480966, 5301568498768, 44351526986704, 372890978840156, 3149155955471690, 26702387443603200, 227238745573918511, 1940201017862028108

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

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

Crossrefs

Cf. A025262, A367044.

Cf. A367041.

Sequence in context: A193236 A357203 A215047 * A346578 A213099 A199259

Adjacent sequences: A367042 A367043 A367044 * A367046 A367047 A367048

Keyword

nonn

Author

Seiichi Manyama, Nov 03 2023

Status

approved