A128816 Number of partitions of an n-element set avoiding the pattern 12|3.

1, 1, 2, 4, 8, 19, 53, 160, 512, 1753, 6431, 25072, 103022, 444145, 2004281, 9447784, 46407476, 236950873, 1254862955, 6880495528, 38999582018, 228195894313, 1376543144453, 8550048509440, 54619642413848, 358490894378881, 2415134218161767, 16686051606437104

Offset

0,3

Links

Table of n, a(n) for n=0..27.

A. M. Goyt, Avoidance of partitions of a 3-element set, arXiv:math/0603481 [math.CO], 2006-2007

Formula

a(0)=1, a(1)=1, a(n) = 1 + a(n-1) + Sum_{k=1..n-2} binomial(n-2, k)*a(n-k-2).

The e.g.f. satisfies the differential equation y'' = y' + y(e^x-1) + e^x.

Crossrefs

Sequence in context: A269023 A173310 A320178 * A006897 A287025 A034767

Adjacent sequences: A128813 A128814 A128815 * A128817 A128818 A128819

Keyword

nonn

Author

Ralf Stephan, May 08 2007

Status

approved