A368936 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^4) ).
1, 2, 7, 30, 142, 715, 3756, 20349, 112865, 637681, 3657075, 21233199, 124562708, 737197980, 4396176336, 26389742175, 159336837840, 967007923321, 5895699043010, 36093405644877, 221785663880176, 1367420967329725, 8456765007380190, 52447676008911675
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\4, (-1)^k*binomial(n+k, k)*binomial(3*n-3*k+1, n-4*k))/(n+1);
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PARI
my(x='x+O('x^30)); Vec(serreverse(x*(1-x)*(1-x+x^4))/x) \\ Michel Marcus, Jan 10 2024
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} (-1)^k * binomial(n+k,k) * binomial(3*n-3*k+1,n-4*k).