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%I #16 Sep 04 2018 12:09:24
%S 1,15,140,1045,6835,40963,230720,1240740,6437890,32468470,160010280,
%T 773624615,3680728375,17274086235,80119845080,367821324040,
%U 1673528845710,7554110698850,33858536700040,150802994850570
%N 5-fold convolution of A001700(n), n >= 0.
%C Fifth column of triangular array A035324.
%H Michael De Vlieger, <a href="/A035330/b035330.txt">Table of n, a(n) for n = 0..1650</a>
%H José Agapito, Ângela Mestre, Maria M. Torres, and Pasquale Petrullo, <a href="http://cs.uwaterloo.ca/journals/JIS/VOL18/Agapito/agapito2.pdf">On One-Parameter Catalan Arrays</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.5.1.
%H Milan Janjić, <a href="https://www.emis.de/journals/JIS/VOL21/Janjic2/janjic103.html">Pascal Matrices and Restricted Words</a>, J. Int. Seq., Vol. 21 (2018), Article 18.5.2.
%F a(n) = (n^2+27*n+122)*binomial(2*(n+5), n+5)/24 - 5*(n+8)*2^(2*n+5) = A035324(n+5, 5);
%F G.f.: c(x)^5/(1-4*x)^(5/2), where c(x) = g.f. for Catalan numbers A000108.
%t Array[(#^2 + 27 # + 122) Binomial[2 (# + 5), # + 5]/24 - 5 (# + 8)*2^(2 # + 5) &, 20, 0] (* _Michael De Vlieger_, Sep 04 2018 *)
%Y Cf. A000108, A045894, A035324.
%K easy,nonn
%O 0,2
%A _Wolfdieter Lang_
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