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%I #12 May 24 2016 10:24:38
%S 1,3,21,162,1365,12219,114156,1100649,10871175,109438830,1118798079,
%T 11583712617,121219182504,1280065637487,13623341795049,
%U 145977237305874,1573536198376401,17051418418204671,185646639499541892
%N A transform of A103210.
%C Partial sums are A166697.
%H G. C. Greubel, <a href="/A166696/b166696.txt">Table of n, a(n) for n = 0..500</a>
%F G.f.: (1-3x+x^2-sqrt(1-14x+27x^2-14x^3+x^4))/(4x);
%F G.f.: 1/(1-3x/((1-x)^2-2x/(1-3x/((1-x)^2-2x/(1-3x/((1-x)^2-2x/(1-3x/(1-... (continued fraction);
%F a(n) = Sum_{k=0..n} (0^(n+k)+C(n+k-1,2k-1))*A103210(k) = 0^n + Sum_{k=0..n} C(n+k-1,2k-1)*A103210(k).
%F Conjecture: (n+1)*a(n) +7*(-2*n+1)*a(n-1) +27*(n-2)*a(n-2) +7*(-2*n+7)*a(n-3) +(n-5)*a(n-4)=0. - _R. J. Mathar_, Feb 10 2015
%p A166696 := proc(n)
%p if n = 0 then
%p 1;
%p else
%p add((0^(n+k)+binomial(n+k-1,2*k-1))*A103210(k),k=0..n) ;
%p end if;
%p end proc: # _R. J. Mathar_, Feb 10 2015
%t CoefficientList[Series[(1 - 3*t + t^2 - Sqrt[1 - 14*t + 27*t^2 - 14*t^3 + t^4])/(4*t), {t, 0, 50}], t] (* _G. C. Greubel_, May 23 2016 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Oct 18 2009
%E A-number in formula corrected by _R. J. Mathar_, Feb 10 2015
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