A372413 Coefficient of x^n in the expansion of ( (1-x+x^3) / (1-x) )^n.
1, 0, 0, 3, 4, 5, 21, 49, 92, 237, 595, 1331, 3169, 7787, 18487, 44108, 107036, 258349, 622371, 1508239, 3658679, 8869465, 21543005, 52399612, 127497281, 310487855, 756858661, 1846060464, 4505442967, 11003284052, 26887642756, 65735882819, 160795695676
Offset: 0
Keywords
Programs
-
PARI
a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(n-2*k-1,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) ).