A174035 A triangle sequence of the form:t(n,m]=Binomial[n, m] + Floor[Eulerian[n + 1, m]/2]

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 17, 39, 17, 1, 1, 33, 161, 161, 33, 1, 1, 66, 610, 1228, 610, 66, 1, 1, 130, 2167, 7844, 7844, 2167, 130, 1, 1, 259, 7332, 44173, 78165, 44173, 7332, 259, 1, 1, 515, 23956, 227680, 655303, 655303, 227680, 23956, 515, 1, 1, 1028, 76363

Offset

0,5

Comments

Row Sums are:

{1, 2, 6, 18, 75, 390, 2582, 20284, 181695, 1814910, 19959422,...}.

Links

Table of n, a(n) for n=0..57.

Formula

t(n,m]=Binomial[n, m] + Floor[Eulerian[n + 1, m]/2]

Example

{1},
{1, 1},
{1, 4, 1},
{1, 8, 8, 1},
{1, 17, 39, 17, 1},
{1, 33, 161, 161, 33, 1},
{1, 66, 610, 1228, 610, 66, 1},
{1, 130, 2167, 7844, 7844, 2167, 130, 1},
{1, 259, 7332, 44173, 78165, 44173, 7332, 259, 1},
{1, 515, 23956, 227680, 655303, 655303, 227680, 23956, 515, 1},
{1, 1028, 76363, 1101864, 4869267, 7862376, 4869267, 1101864, 76363, 1028, 1}

Mathematica

<< DiscreteMath`Combinatorica`
Table[Table[Binomial[n, m] + Floor[Eulerian[n + 1, m] 2], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A100754 A332307 A296405 * A303888 A305281 A304894

Adjacent sequences: A174032 A174033 A174034 * A174036 A174037 A174038

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 06 2010

Status

approved