A188478 Binomial variation of the Catalan numbers

1, 1, 1, 2, 4, 11, 33, 116, 456, 1999, 9623, 50603, 288287, 1769352, 11636669, 81652911, 608857325, 4807873069, 40080193414, 351751992542, 3241754135966, 31301851579056, 316012152140592, 3329322705562603, 36539984716325869, 417102552119591395, 4944630222121834001, 60791493200390178470

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

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

Mathematica

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}]

Crossrefs

A000108, A001147, A188479

Sequence in context: A268320 A127782 A002846 * A302547 A123444 A123473

Adjacent sequences: A188475 A188476 A188477 * A188479 A188480 A188481

Keyword

nonn,easy

Author

Olivier Gérard, Apr 01 2011

Status

approved