A371542 G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1+x))^3.

1, 3, 9, 34, 141, 621, 2849, 13467, 65127, 320686, 1602294, 8103087, 41397186, 213331026, 1107604764, 5788249329, 30422897664, 160717169622, 852894534042, 4544635033164, 24305345593290, 130423538829518, 701994030831654, 3788979493701069, 20503322609731348

Offset: 0

Author

Seiichi Manyama, Mar 26 2024

Keywords

• nonn

Crossrefs

Cf. A127897, A370720, A371494.

Cf. A371495, A371538.

Cf. A371516.

Programs

PARI

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

Formula

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

From Seiichi Manyama, Dec 10 2024: (Start)

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

G.f. A(x) satisfies A(x) = 1 + x * (1 + A(x)^(4/3) + A(x)^(5/3)).

G.f.: A(x) = (1 + B(x))^3 where B(x) is the g.f. of A127897. (End)