# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a186183 Showing 1-1 of 1 %I A186183 #18 Sep 22 2024 06:08:19 %S A186183 1,1,2,9,68,646,6857,77695,919642,11233858,140544189,1791614714, %T A186183 23187320736,303861373679,4023883823059,53762917329659, %U A186183 723854999871943,9811154512175468,133762940465746744,1833187046654598058,25239961633188882896 %N A186183 Expansion of 1/(1-x*A002295(x)). %H A186183 Vaclav Kotesovec, Recurrence of order 6 %H A186183 Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013. %F A186183 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 A186183 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 A186183 a:= n-> `if` (n=0, 1, add (k/(5*n-4*k) *binomial (6*n-5*k-1, n-k), k=1..n)): %p A186183 seq (a(n), n=0..30); %o A186183 (PARI) a(n)=max(1,sum(k=1,n, k/(5*n-4*k)*binomial(6*n-5*k-1,n-k))) %K A186183 nonn %O A186183 0,3 %A A186183 _Vladimir Kruchinin_, Feb 14 2011 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE