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Binomial variation of the Catalan numbers
2

%I #11 Oct 24 2012 03:16:00

%S 1,1,1,2,4,11,33,116,456,1999,9623,50603,288287,1769352,11636669,

%T 81652911,608857325,4807873069,40080193414,351751992542,3241754135966,

%U 31301851579056,316012152140592,3329322705562603,36539984716325869,417102552119591395,4944630222121834001,60791493200390178470

%N Binomial variation of the Catalan numbers

%H Vincenzo Librandi, <a href="/A188478/b188478.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = sum( binomial(n-1-i, i)*a(i)*a(n-1-i), i=0..(n-1) ) with a(0)=1

%t a[0] = 1; a[n_] := a[n] = Sum[ Binomial[n - i - 1, i] a[i]*a[n - 1 - i], {i, 0, n - 1}]; Table[a[i], {i, 0, 30}]

%Y A000108, A001147, A188479

%K nonn,easy

%O 0,4

%A _Olivier GĂ©rard_, Apr 01 2011