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A186182 Expansion of 1/(1-x*A002294(x)). 0

%I #19 Oct 30 2022 10:05:32

%S 1,1,2,8,50,388,3363,31132,301156,3007000,30753169,320492869,

%T 3391067666,36331532588,393353506931,4296895624750,47300050998991,

%U 524168531729460,5842914510975105,65470405191871331,737008925038212059,8331166456981245521

%N Expansion of 1/(1-x*A002294(x)).

%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/(4*n-3*k)*binomial(5*n-4*k-1,n-k), n>0; a(0) = 1.

%t Join[{1},Table[Sum[k/(4n-3k) Binomial[5n-4k-1,n-k],{k,n}],{n,30}]] (* _Harvey P. Dale_, Feb 05 2012 *)

%o (PARI) a(n)=max(1,sum(k=1,n, k/(4*n-3*k)*binomial(5*n-4*k-1,n-k)))

%Y Cf. A002294.

%K nonn

%O 0,3

%A _Vladimir Kruchinin_, Feb 14 2011

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Last modified February 23 11:40 EST 2024. Contains 370283 sequences. (Running on oeis4.)