%I #18 Sep 22 2024 06:08:19

%S 1,1,2,9,68,646,6857,77695,919642,11233858,140544189,1791614714,

%T 23187320736,303861373679,4023883823059,53762917329659,

%U 723854999871943,9811154512175468,133762940465746744,1833187046654598058,25239961633188882896

%N Expansion of 1/(1-x*A002295(x)).

%H Vaclav Kotesovec, <a href="/A186183/a186183.txt">Recurrence of order 6</a>

%H Vladimir Kruchinin and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.

%F 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.

%F 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

%p a:= n-> `if` (n=0, 1, add (k/(5*n-4*k) *binomial (6*n-5*k-1, n-k), k=1..n)):

%p seq (a(n), n=0..30);

%o (PARI) a(n)=max(1,sum(k=1,n, k/(5*n-4*k)*binomial(6*n-5*k-1,n-k)))

%K nonn

%O 0,3

%A _Vladimir Kruchinin_, Feb 14 2011