A174693 A symmetrical triangle sequence: t(n,m)=n!*Binomial[n, m]*Eulerian[n + 1, m] - n! + 1

1, 1, 1, 1, 15, 1, 1, 193, 193, 1, 1, 2473, 9481, 2473, 1, 1, 34081, 362281, 362281, 34081, 1, 1, 517681, 12862081, 34789681, 12862081, 517681, 1, 1, 8709121, 454366081, 2755186561, 2755186561, 454366081, 8709121, 1, 1, 161884801

Offset

0,5

Comments

Row sums are:

{1, 2, 17, 388, 14429, 792726, 61549207, 6436523528, 872588545929,

148833116409610, 31190020579065611,...}.

Links

Table of n, a(n) for n=0..37.

Formula

t(n,m)=n!*Binomial[n, m]*Eulerian[n + 1, m] - n! + 1

Example

{1},
{1, 1},
{1, 15, 1},
{1, 193, 193, 1},
{1, 2473, 9481, 2473, 1},
{1, 34081, 362281, 362281, 34081, 1},
{1, 517681, 12862081, 34789681, 12862081, 517681, 1},
{1, 8709121, 454366081, 2755186561, 2755186561, 454366081, 8709121, 1},
{1, 161884801, 16491807361, 199225272961, 440830615681, 199225272961, 16491807361, 161884801, 1},
{1, 3308014081, 624966088321, 13875125765761, 59913158336641, 59913158336641, 13875125765761, 624966088321, 3308014081, 1},
{1, 73878739201, 24925007923201, 959522066899201, 7420910293843201, 14379158084256001, 7420910293843201, 959522066899201, 24925007923201, 73878739201, 1}

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_] =n!*Binomial[n, m]*Eulerian[n + 1, m] - n! + 1;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A155493 A156939 A174187 * A340430 A022178 A176639

Adjacent sequences: A174690 A174691 A174692 * A174694 A174695 A174696

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 27 2010

Status

approved