A369600 Expansion of (1/x) * Series_Reversion( x * (1/(1+x)^3 - x^3) ).
1, 3, 12, 56, 291, 1638, 9780, 60948, 391821, 2577575, 17256918, 117150228, 804343302, 5575177026, 38957753136, 274143594685, 1941037464402, 13818185220783, 98848503602394, 710185896393792, 5122358166219855, 37076879861508830, 269235792063692580
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x)^3-x^3))/x) -
PARI
a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(3*n+3*k+3, n-3*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(3*n+3*k+3,n-3*k).