A174692 A symmetrical triangle sequence: t(n,m)=n!*Eulerian[n + 1, m]^2 - n! + 1

1, 1, 1, 1, 31, 1, 1, 721, 721, 1, 1, 16201, 104521, 16201, 1, 1, 389761, 10944361, 10944361, 389761, 1, 1, 10367281, 1021305601, 4202679601, 1021305601, 10367281, 1, 1, 307480321, 92886433921, 1229523926401, 1229523926401, 92886433921

Offset

0,5

Comments

Row sums are:

{1, 2, 33, 1444, 136925, 22668246, 6266025367, 2645435681288,

1628649184821129, 1398189017071123210, 1620879822232935264011,...}.

Links

Table of n, a(n) for n=0..33.

Formula

t(n,m)=n!*Eulerian[n + 1, m]^2 - n! + 1

Example

{1},
{1, 1},
{1, 31, 1},
{1, 721, 721, 1},
{1, 16201, 104521, 16201, 1},
{1, 389761, 10944361, 10944361, 389761, 1},
{1, 10367281, 1021305601, 4202679601, 1021305601, 10367281, 1},
{1, 307480321, 92886433921, 1229523926401, 1229523926401, 92886433921, 307480321, 1},
{1, 10160760961, 8604032492161, 313900826601601, 983619145111681, 313900826601601, 8604032492161, 10160760961, 1},
{1, 372375843841, 830510972565121, 75188647770445441, 623074977416707201, 623074977416707201, 75188647770445441, 830510972565121, 372375843841, 1},
{1, 15042446496001, 84543977513318401, 17619128067859718401, 344122240288359456001, 897227967480577286401, 344122240288359456001, 17619128067859718401, 84543977513318401, 15042446496001, 1}

Mathematica

<< DiscreteMath`Combinatorica`
t[n_, m_] = n!*Eulerian[n + 1, m]^2 - n! + 1;
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A040961 A300656 A239633 * A172302 A103474 A047687

Adjacent sequences: A174689 A174690 A174691 * A174693 A174694 A174695

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 27 2010

Status

approved