OFFSET
0,3
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..600
FORMULA
a(n) = (1/n) * Sum_{k=0..n-1} binomial(n,k) * binomial(2*n+3*k,n-1-k) for n > 0.
G.f.: 1 + Series_Reversion( x / ((1+x)^2 * (1+x*(1+x)^3)) ). - Seiichi Manyama, Oct 07 2025
MATHEMATICA
a[n_]:=Sum[(1/n)*Binomial[n, k]*Binomial[2*n+3*k, n-1-k], {k, 0, n-1}]; Table[a[n], {n, 0, 30}] (* Vincenzo Librandi, Oct 23 2025 *)
PROG
(PARI) a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(2*n+3*k, n-1-k))/n);
(Magma) [1] cat [&+[Binomial(n, k) * Binomial(2*n+3*k, n-1-k) *(1/n): k in [0..n-1]] : n in [1..30]]; // Vincenzo Librandi, Oct 23 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 05 2023
STATUS
approved