A387496 - OEIS

A387496

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

1, 2, 6, 23, 99, 453, 2159, 10607, 53348, 273335, 1421622, 7485986, 39831697, 213823040, 1156633157, 6298316994, 34497786312, 189935384460, 1050571453196, 5835053803539, 32530313625482, 181972092601480, 1021089103780963, 5745802113774112, 32416467431257797, 183324417201552542

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

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+1,k) * binomial(2*n+k+2,n-2*k).

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

MATHEMATICA

Table[SeriesCoefficient[((1+x)^2*(1+x^2*(1+x)))^(n+1), {x, 0, n}]/(n+1), {n, 0, 30}] (* Vincenzo Librandi, Oct 20 2025 *)

PROG

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+x^2*(1+x))))/x)