A369401 Expansion of (1/x) * Series_Reversion( x / (1+x) * (1-x^3)^3 ).
1, 1, 1, 4, 16, 46, 139, 511, 1891, 6707, 24366, 91840, 348236, 1320309, 5056414, 19565036, 76077330, 296994727, 1165438921, 4594915664, 18181401268, 72176250259, 287450966807, 1148178877918, 4598148937702, 18458646079181, 74267340207247
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x)*(1-x^3)^3)/x) -
PARI
a(n, s=3, t=3, u=1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial(u*(n+1), n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(3*n+k+2,k) * binomial(n+1,n-3*k).
a(n) = (1/(n+1)) * [x^n] ( (1+x) / (1-x^3)^3 )^(n+1). - Seiichi Manyama, Feb 16 2024