A389346 Expansion of (1/x) * Series_Reversion( x * (1 - x^2 / (1 - x)^4) ).

1, 0, 1, 4, 13, 48, 191, 776, 3219, 13628, 58600, 255124, 1122519, 4983796, 22299627, 100454036, 455212313, 2073680196, 9490802309, 43620240660, 201241963152, 931624173296, 4326349259236, 20148605015184, 94082571239825, 440376748997612, 2065908139983961, 9711765277023280

Offset

0,4

Links

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

Formula

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

a(n) = (1/(n+1)) * [x^n] 1/(1 - x^2 / (1 - x)^4)^(n+1).

Mathematica

Table[SeriesCoefficient[1/(1-x^2/(1-x)^4)^(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^2/(1-x)^4))/x)
(Magma) [1/(n+1)*&+[Binomial(n+k, k)*Binomial(n+2*k-1, n-2*k): k in [0..Floor(n/2)]]: n in [0..35]]; // Vincenzo Librandi, Oct 18 2025

Crossrefs

Cf. A000957, A046736, A389345, A389347.

Cf. A389247.

Sequence in context: A357642 A149448 A149449 * A149450 A297591 A294298

Adjacent sequences: A389343 A389344 A389345 * A389347 A389348 A389349

Keyword

nonn

Author

Seiichi Manyama, Oct 01 2025

Status

approved