login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A367260
G.f. satisfies A(x) = 1 + x*A(x)^3 * (1 + x*A(x))^3.
0
1, 1, 6, 36, 251, 1881, 14817, 120950, 1014042, 8680377, 75552553, 666614637, 5948817600, 53599239101, 486926148000, 4455202562652, 41018936164660, 379747493741643, 3532914858433284, 33012260400580342, 309692626084981245, 2915659701275923491
OFFSET
0,3
FORMULA
If g.f. satisfies A(x) = 1 + x*A(x)^t * (1 + x*A(x)^u)^s, then a(n) = Sum_{k=0..n} binomial(t*k+u*(n-k)+1,k) * binomial(s*k,n-k) / (t*k+u*(n-k)+1).
PROG
(PARI) a(n, s=3, t=3, u=1) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 11 2023
STATUS
approved