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A174693 A symmetrical triangle sequence: t(n,m)=n!*Binomial[n, m]*Eulerian[n + 1, m] - n! + 1 0
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A022178 A176639 A015139

Adjacent sequences:  A174690 A174691 A174692 * A174694 A174695 A174696

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 27 2010

STATUS

approved

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Last modified December 15 03:08 EST 2017. Contains 296020 sequences.