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A030055 a(n) = binomial(2*n+1, n-5).

%I A030055 #26 Sep 08 2022 08:44:50
%S A030055 1,13,105,680,3876,20349,100947,480700,2220075,10015005,44352165,
%T A030055 193536720,834451800,3562467300,15084504396,63432274896,265182149218,
%U A030055 1103068603890,4568648125690,18851684897584
%N A030055 a(n) = binomial(2*n+1, n-5).
%H A030055 G. C. Greubel, <a href="/A030055/b030055.txt">Table of n, a(n) for n = 5..1000</a>
%H A030055 Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>.
%F A030055 G.f.: x^5*2048/((1-sqrt(1-4*x))^11*sqrt(1-4*x))+(-1/x^6+9/x^5-28/x^4+35/x^3-15/x^2+1/x). - _Vladimir Kruchinin_, Aug 11 2015
%F A030055 From _Amiram Eldar_, Jan 24 2022: (Start)
%F A030055 Sum_{n>=5} 1/a(n) = 9497/1260 - 32*Pi/(9*sqrt(3)).
%F A030055 Sum_{n>=5} (-1)^(n+1)/a(n) = 9392*log(phi)/(5*sqrt(5)) - 508169/1260, where phi is the golden ratio (A001622). (End)
%p A030055 seq(binomial(2*n+1,n-5),n=5..25); # _Muniru A Asiru_, Oct 24 2018
%t A030055 Table[Binomial[2*n+1, n-5], {n, 5, 30}] (* _G. C. Greubel_, Oct 23 2018 *)
%o A030055 (PARI) vector(30, n, m=n+4; binomial(2*m+1,m-5)) \\ _Michel Marcus_, Aug 11 2015
%o A030055 (Magma) [Binomial(2*n+1, n-5): n in [5..30]]; // _G. C. Greubel_, Oct 23 2018
%o A030055 (GAP) List([5..25],n->Binomial(2*n+1,n-5)); # _Muniru A Asiru_, Oct 24 2018
%Y A030055 Diagonal 12 of triangle A100257.
%Y A030055 Cf. A001622.
%K A030055 nonn
%O A030055 5,2
%A A030055 _N. J. A. Sloane_