A369481 Expansion of (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^3)) ).
1, 2, 5, 15, 51, 187, 718, 2844, 11530, 47612, 199576, 847013, 3632468, 15717041, 68527255, 300780438, 1327939406, 5893299392, 26275243626, 117635107818, 528631769323, 2383660351991, 10781500113896, 48903885040638, 222400899237943, 1013841791472632
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x+x^3)))/x) -
PARI
a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(2*n-k+2,n-3*k).