A370214 Coefficient of x^n in the expansion of ( (1+x) / (1-x^3)^2 )^n.
1, 1, 1, 7, 33, 101, 319, 1226, 4705, 17017, 61901, 231837, 872031, 3260856, 12220846, 46062632, 174030177, 657910813, 2490889801, 9448650829, 35890996733, 136473161741, 519476028237, 1979421705602, 7549358718559, 28816041869476, 110075383797016
Offset: 0
Keywords
Crossrefs
Cf. A369399.
Programs
-
PARI
a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial(u*n, n-s*k));
Formula
a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(n,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^3)^2 ). See A369399.