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Expansion of 1/(1 - x*A002296(x)).
2

%I #20 Sep 23 2024 04:24:36

%S 1,1,2,10,89,1002,12592,168805,2363241,34138860,505042286,7612594936,

%T 116492572621,1804984878387,28260999959595,446441276449715,

%U 7106718529937710,113886198966545724

%N Expansion of 1/(1 - x*A002296(x)).

%H Vaclav Kotesovec, <a href="/A186184/a186184.txt">Recurrence of order 7</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/(6*n-5*k))*binomial(7*n-6*k-1, n-k), n > 0.

%p A186184 := proc(n)

%p if n = 0 then

%p 1;

%p else

%p add( k/(6*n-5*k)*binomial(7*n-6*k-1,n-k), k=1..n) ;

%p end if;

%p end proc:

%p seq(A186184(n),n=0..20) ; # _R. J. Mathar_, Feb 26 2011

%t Join[{1},Table[Sum[k/(6n-5k) Binomial[7n-6k-1,n-k],{k,n}],{n,30}]] (* _Harvey P. Dale_, Aug 29 2012 *)

%K nonn

%O 0,3

%A _Vladimir Kruchinin_, Feb 14 2011