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A186184 Expansion of 1/(1 - x*A002296(x)).

%I A186184 #24 Feb 19 2025 10:25:33
%S A186184 1,1,2,10,89,1002,12592,168805,2363241,34138860,505042286,7612594936,
%T A186184 116492572621,1804984878387,28260999959595,446441276449715,
%U A186184 7106718529937710,113886198966545724
%N A186184 Expansion of 1/(1 - x*A002296(x)).
%H A186184 Vaclav Kotesovec, <a href="/A186184/a186184.txt">Recurrence of order 7</a>
%H A186184 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 A186184 a(n) = Sum_{k=1..n} (k/(6*n-5*k))*binomial(7*n-6*k-1, n-k), n > 0.
%p A186184 A186184 := proc(n)
%p A186184    if n = 0 then
%p A186184       1;
%p A186184    else
%p A186184       add( k/(6*n-5*k)*binomial(7*n-6*k-1,n-k), k=1..n) ;
%p A186184    end if;
%p A186184 end proc:
%p A186184 seq(A186184(n),n=0..20) ; # _R. J. Mathar_, Feb 26 2011
%t A186184 Join[{1},Table[Sum[k/(6n-5k) Binomial[7n-6k-1,n-k],{k,n}],{n,30}]] (* _Harvey P. Dale_, Aug 29 2012 *)
%Y A186184 Cf. A002296.
%K A186184 nonn
%O A186184 0,3
%A A186184 _Vladimir Kruchinin_, Feb 14 2011