A369011 Expansion of (1/x) * Series_Reversion( x * (1-x^3/(1-x))^2 ).

1, 0, 0, 2, 2, 2, 17, 36, 59, 240, 669, 1452, 4538, 13574, 34505, 99816, 299112, 825768, 2364715, 7023466, 20182611, 58327250, 172491553, 505163444, 1476966513, 4370772096, 12924382671, 38149522136, 113266357609, 336894290910, 1001473479313, 2985508193930

Offset: 0

Author

Seiichi Manyama, Jan 11 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for reversions of series

Crossrefs

Cf. A211789, A368957.

Cf. A054514, A369014.

Cf. A368962, A368966, A368968.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1-x^3/(1-x))^2)/x)

PARI

a(n, s=3, t=2, u=-2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);

Formula

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