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%I #15 Mar 17 2017 22:52:50
%S 1,1,1,1,1,1,1,6,11,76,911,70146,63973151,4487524623191,
%T 47846849137190094661,19519446695048425827542253313671,
%U 12288737121834287082853490635842863813970134234101
%N a(n) = (1 + Sum_{j=1..K-2} a(n-j)*a(n-j-1))/a(n-K) with a(1),...,a(K)=1, where K=7.
%H Seiichi Manyama, <a href="/A283820/b283820.txt">Table of n, a(n) for n = 1..23</a>
%H Matthew Christopher Russell, <a href="http://www.math.rutgers.edu/~zeilberg/Theses/MatthewRussellThesis.pdf">Using experimental mathematics to conjecture and prove theorems in the theory of partitions and commutative and non-commutative recurrences</a>, PhD Dissertation, Mathematics Department, Rutgers University, May 2016; see <a href="https://pdfs.semanticscholar.org/fdeb/e20954dacb7ec7a24afe2cf491b951c5a28d.pdf">also</a>.
%t a[n_]:=If[n<8, 1, (1 + Sum[a[n - j] * a[n - j - 1], {j, 5}])/a[n - 7]]; Table[a[n], {n, 1, 17}] (* _Indranil Ghosh_, Mar 17 2017 *)
%o (PARI) a(n) = if(n<8, 1, (1 + sum(j=1, 5, a(n - j) * a(n - j - 1)))/a(n - 7));
%o for(n=1, 17, print1(a(n),", ")) \\ _Indranil Ghosh_, Mar 17 2017
%K nonn
%O 1,8
%A _N. J. A. Sloane_, Mar 17 2017
%E More terms from _Indranil Ghosh_, Mar 17 2017
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