A389437 Expansion of (1/x) * Series_Reversion( x * (1 - x * (1 + x)^2) / (1 + x) ).

1, 2, 8, 41, 235, 1443, 9283, 61756, 421378, 2932711, 20738719, 148584710, 1076253482, 7868354479, 57984899719, 430281137466, 3212367264492, 24111672658844, 181845683770086, 1377324789135958, 10472338584424346, 79903749472436127, 611604051769429491

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

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

a(n) = (1/(n+1)) * [x^n] ((1 + x) / (1 - x * (1 + x)^2))^(n+1).

Mathematica

Table[SeriesCoefficient[((1+x)/(1-x*(1+x)^2))^(n+1), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 18 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x*(1+x)^2)/(1+x))/x)
(Magma) [1/(n+1)*&+[Binomial(n+k, k)*Binomial(n+2*k+1, n-k): k in [0..n]]: n in [0..35]]; // Vincenzo Librandi, Oct 18 2025

Crossrefs

Cf. A006318, A007863, A389438.

Sequence in context: A060436 A020083 A333093 * A389548 A217362 A389629

Adjacent sequences: A389434 A389435 A389436 * A389438 A389439 A389440

Keyword

nonn

Author

Seiichi Manyama, Oct 04 2025

Status

approved