A369621 Expansion of (1/x) * Series_Reversion( x / (1/(1-x) + x^3) ).
1, 1, 2, 6, 18, 57, 191, 660, 2334, 8417, 30831, 114380, 428915, 1623143, 6190876, 23774613, 91849846, 356735941, 1392091107, 5455425618, 21460947111, 84717452192, 335479515201, 1332327233554, 5305235886691, 21176621863427, 84720103674498
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)+x^3))/x) -
PARI
a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(2*n-4*k, n-3*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(2*n-4*k,n-3*k).