A369399 Expansion of (1/x) * Series_Reversion( x / (1+x) * (1-x^3)^2 ).
1, 1, 1, 3, 11, 31, 86, 277, 937, 3095, 10275, 35091, 121662, 423286, 1481648, 5232315, 18601843, 66436069, 238327939, 858805613, 3106856141, 11277393837, 41062303214, 149948280259, 549027748390, 2015108865850, 7412690394406, 27324968423054
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)^2)/x) -
PARI
a(n, s=3, t=2, 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(2*n+k+1,k) * binomial(n+1,n-3*k).
a(n) = (1/(n+1)) * [x^n] ( (1+x) / (1-x^3)^2 )^(n+1). - Seiichi Manyama, Feb 16 2024