A372371 Coefficient of x^n in the expansion of ( (1+x+x^3)^2 / (1+x) )^n.
1, 1, 1, 7, 25, 61, 187, 666, 2137, 6676, 22001, 73217, 239923, 789517, 2624182, 8729527, 29026553, 96790606, 323546416, 1082566763, 3626148425, 12163438539, 40847087821, 137294721676, 461890741843, 1555264438186, 5240857508017, 17672768973979, 59634361740734
Offset: 0
Keywords
Programs
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PARI
a(n, s=3, t=2, u=-1) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(n-k,n-3*k).
The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1+x) / (1+x+x^3)^2 ). See A372375.