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%I #36 Sep 08 2022 08:44:35
%S 1,20,210,1680,11550,72072,420420,2333760,12471030,64664600,327202876,
%T 1622493600,7909656300,38003792400,180324117000,846321189120,
%U 3934071152550,18132120329400,82937661506700
%N Expansion of (1+6*x)/(1-4*x)^(7/2).
%C Fourth column in A104684. - _Paul Barry_, May 02 2005
%H Vincenzo Librandi, <a href="/A007744/b007744.txt">Table of n, a(n) for n = 0..100</a>
%H Ömür Deveci and Anthony G. Shannon, <a href="https://doi.org/10.20948/mathmontis-2021-50-4">Some aspects of Neyman triangles and Delannoy arrays</a>, Mathematica Montisnigri (2021) Vol. L, 36-43.
%H A. Petojevic and N. Dapic, <a href="http://www.mi.sanu.ac.rs/~gvm/radovi/AP-Budva.pdf">The vAm(a,b,c;z) function</a>, Preprint 2013.
%H G. Thimm, <a href="/A007741/a007741.pdf">Emails to N. J. A. Sloane, Sep. 1994</a>
%F a(n) = binomial(2n+3, n) * binomial(n+3, 3). - _Paul Barry_, May 02 2005
%F G.f.: G(0) where G(k) = 1 + 4*x*(k+1)*(4*k+5)/((2*k+1)^2 - x*(2*k+1)^2*(2*k+3)*(4*k+7)/(x*(2*k+3)*(4*k+7) + 2*(k+1)^2/G(k+1))); (continued fraction, 3rd kind, 3-step). - Sergei N. Gladkovskii, Jul 12 2012
%F D-finite with recurrence: n*a(n) + 2*(n-11)*a(n-1) + 12*(-2*n-1)*a(n-2) = 0. - _R. J. Mathar_, Nov 24 2012
%t Array[Binomial[2 # + 3, #]*Binomial[# + 3, 3] &, 19, 0] (* _Michael De Vlieger_, Aug 18 2021 *)
%o (Magma) [Binomial(2*n+3, n)*Binomial(n+3, 3): n in [0..20]]; // _Vincenzo Librandi_, Aug 20 2011
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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