OFFSET
0,3
LINKS
Vaclav Kotesovec, Recurrence of order 6
Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
a(n) = Sum_{k=1..n} k/(5*n-4*k) * binomial(6*n-5*k-1,n-k) if n>0; a(0)=1.
a(n) ~ 2^(6*n+4) * 3^(6*n + 9/2) / (51136801 * sqrt(Pi) * n^(3/2) * 5^(5*n - 7/2)). - Vaclav Kotesovec, Sep 22 2024
MAPLE
a:= n-> `if` (n=0, 1, add (k/(5*n-4*k) *binomial (6*n-5*k-1, n-k), k=1..n)):
seq (a(n), n=0..30);
PROG
(PARI) a(n)=max(1, sum(k=1, n, k/(5*n-4*k)*binomial(6*n-5*k-1, n-k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Feb 14 2011
STATUS
approved