A369622 Expansion of (1/x) * Series_Reversion( x / (1/(1-x)^2 + x^3) ).
1, 2, 7, 31, 151, 783, 4243, 23740, 136099, 795321, 4719980, 28370532, 172357487, 1056658346, 6528779587, 40614467912, 254167595939, 1599012530917, 10107091256418, 64155246033712, 408780285886008, 2613634555525584, 16763436345211527, 107827070566159112
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)^2+x^3))/x) -
PARI
a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(3*n-5*k+1, n-3*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(3*n-5*k+1,n-3*k).