OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(2*n,k) * binomial(2*n-2*k-1,n-2*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^2)^2 ). See A369226.
PROG
(PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((u+1)*n-s*k-1, n-s*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 13 2024
STATUS
approved