A369297 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x^3) ).
1, 2, 7, 31, 153, 806, 4440, 25266, 147364, 876282, 5292527, 32378125, 200218715, 1249456536, 7858638756, 49766595855, 317051378103, 2030589300596, 13066646029059, 84439101344619, 547746622599561, 3565472378360110, 23282050305073680, 152466688160732190
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x^3))/x) -
PARI
a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(3*n-3*k+1,n-3*k).
a(n) = (1/(n+1)) * [x^n] 1/( (1-x)^2 * (1-x^3) )^(n+1). - Seiichi Manyama, Feb 14 2024