A264663 Catalan numbers written in base 2.

1, 1, 10, 101, 1110, 101010, 10000100, 110101101, 10110010110, 1001011111110, 100000110011100, 1110010110100010, 110010110010001100, 10110101010111110100, 1010001100111100001000, 100100111110111001111101, 10000110111000001111100110, 111101110100011100011110110, 11100011110000011000000101100

Offset: 0

Author

Ilya Gutkovskiy, Nov 20 2015

Keywords

• nonn
• base

Links

• Eric Weisstein's World of Mathematics, Catalan Number
• Eric Weisstein's World of Mathematics, Binary

Crossrefs

Cf. A000108, A004676, A004685.

Programs

Magma

[Seqint(Intseq(Catalan(n), 2)): n in [0..20]]; // Vincenzo Librandi, Nov 21 2015

Mathematica

Table[FromDigits[IntegerDigits[CatalanNumber[n], 2]], {n, 0, 18}]

PARI

vector(30, n, n--; subst(Pol(binary(binomial(2*n,n)/(n+1))), 'x, 10)) \\ Altug Alkan, Nov 20 2015

Formula

a(n) = A007088(A000108(n)).