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A252766 a(n) = n-th number of the n-th iteration of the hyperbinomial transform on the sequence of 1's.

%I A252766 #4 Dec 21 2014 10:44:54
%S A252766 1,2,13,163,2993,71801,2120545,74300269,3010775745,138473150833,
%T A252766 7125155956601,405508439303573,25289672996300113,1715033239186419673,
%U A252766 125649446059365470481,9889850149432716471301,832278360169843776972545,74571018189601103968946273
%N A252766 a(n) = n-th number of the n-th iteration of the hyperbinomial transform on the sequence of 1's.
%H A252766 Alois P. Heinz, <a href="/A252766/b252766.txt">Table of n, a(n) for n = 0..350</a>
%F A252766 a(n) = Sum_{j=0..n} n * (2*n-j)^(n-j-1) * C(n,j) for n>0, a(0) = 1.
%p A252766 a:= n-> `if`(n=0, 1, add(n*(2*n-j)^(n-j-1)*binomial(n, j), j=0..n)):
%p A252766 seq(a(n), n=0..20);
%Y A252766 Main diagonal of A144303.
%K A252766 nonn
%O A252766 0,2
%A A252766 _Alois P. Heinz_, Dec 21 2014