A188479 Binomial variation of the Catalan Numbers

1, 1, 2, 4, 12, 40, 156, 700, 3520, 19592, 119992, 801272, 5792464, 45071600, 375615696, 3338063600, 31511918816, 314913425280, 3321357021600, 36868596345056, 429672869359360, 5245439731918784, 66941714022827072, 891387254398818752, 12363478873222765568, 178331546692362644992, 2671094825005048612224

Offset

0,3

Links

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

Formula

a(n) = sum( binomial(n-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, i] a[i]*a[n-1-i], {i, 0, n-1}]; Table[ a[n], {n, 0, 30}]

Crossrefs

A000108, A001147, A188478

Sequence in context: A215073 A215074 A215070 * A062962 A033472 A134983

Adjacent sequences: A188476 A188477 A188478 * A188480 A188481 A188482

Keyword

nonn,easy

Author

Olivier Gérard, Apr 01 2011

Status

approved