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Perfect powers that appear more than once in the Catalan triangle.
1

%I #17 Feb 04 2020 21:41:47

%S 9,27,324,8000,11025,374544,12723489,432224100,14682895929,

%T 498786237504,16944049179225,575598885856164,19553418069930369,

%U 664240615491776400,22564627508650467249,766533094678624110084

%N Perfect powers that appear more than once in the Catalan triangle.

%C Since every integer appears exactly once in the first column of the Catalan triangle, this sequence lists perfect powers that appear in any other column of the triangle. Pell's equation can be used to prove that infinitely many perfect squares appear in this sequence.

%H Nathaniel Benjamin, Grant Fickes, Eugene Fiorini, Edgar Jaramillo Rodriguez, Eric Jovinelly, Tony W. H. Wong, <a href="https://www.emis.de/journals/JIS/VOL22/Fiorini/fiorini3.html">Primes and Perfect Powers in the Catalan Triangle</a>, J. Int. Seq., Vol. 22 (2019), Article 19.7.6.

%H Eric Jovinelly, <a href="/A317027/a317027.txt">Python program</a>

%Y Cf. A009766.

%Y Subsequence of A275586.

%K nonn,more

%O 1,1

%A _Eric Jovinelly_, _Eugene Fiorini_, Jul 19 2018

%E a(9)-a(16) from _Giovanni Resta_, Jul 29 2018