OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(4*n-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)^3 - x^3) ). See A369114.
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n+k-1, k)*binomial(4*n-1, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 13 2024
STATUS
approved