A174691 A symmetrical triangle sequence: t(n,m)=n!*Eulerian[n + 1, m] - n! + 1

1, 1, 1, 1, 7, 1, 1, 61, 61, 1, 1, 601, 1561, 601, 1, 1, 6721, 36121, 36121, 6721, 1, 1, 85681, 856801, 1738801, 856801, 85681, 1, 1, 1239841, 21631681, 78714721, 78714721, 21631681, 1239841, 1, 1, 20200321, 588954241, 3557554561, 6297540481

Offset

0,5

Comments

Row sums are:

{1, 2, 9, 124, 2765, 85686, 3623767, 203172488, 14630958729, 1316815315210,

144850043923211,...}.

Links

Table of n, a(n) for n=0..40.

Formula

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

Example

{1},
{1, 1},
{1, 7, 1},
{1, 61, 61, 1},
{1, 601, 1561, 601, 1},
{1, 6721, 36121, 36121, 6721, 1},
{1, 85681, 856801, 1738801, 856801, 85681, 1},
{1, 1239841, 21631681, 78714721, 78714721, 21631681, 1239841, 1},
{1, 20200321, 588954241, 3557554561, 6297540481, 3557554561, 588954241, 20200321, 1},
{1, 367234561, 17359816321, 165179710081, 475500896641, 475500896641, 165179710081, 17359816321, 367234561, 1},
{1, 7384608001, 553885516801, 7996013625601, 35337664454401, 57060147513601, 35337664454401, 7996013625601, 553885516801, 7384608001, 1}

Mathematica

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

Crossrefs

Sequence in context: A176392 A015118 A340428 * A156692 A188644 A331899

Adjacent sequences: A174688 A174689 A174690 * A174692 A174693 A174694

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 27 2010

Status

approved