A174036 A triangle sequence of the form:t(n,m]=If[m == 0 || m == n, 1, Binomial[Eulerian[n + 1, m], If[Floor[n/2] < m, n - m, m]]]

1, 1, 1, 1, 4, 1, 1, 11, 11, 1, 1, 26, 2145, 26, 1, 1, 57, 45451, 45451, 57, 1, 1, 120, 708645, 2347470160, 708645, 120, 1, 1, 247, 9212778, 634928765569, 634928765569, 9212778, 247, 1, 1, 502, 106689528, 114483233476184, 24796191085864033165

Offset

0,5

Comments

Row Sums are:

{1, 2, 6, 24, 2199, 91018, 2348887692, 1269875957190, 24796420052544365595,

245680889601030693796100, 8010653420480145498314047991192574,...}.

Links

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

Formula

t(n,m]=If[m == 0 || m == n, 1, Binomial[Eulerian[n + 1, m], If[Floor[n/2] < m, n - m, m]]]

Example

{1},
{1, 1},
{1, 4, 1},
{1, 11, 11, 1},
{1, 26, 2145, 26, 1},
{1, 57, 45451, 45451, 57, 1},
{1, 120, 708645, 2347470160, 708645, 120, 1},
{1, 247, 9212778, 634928765569, 634928765569, 9212778, 247, 1},
{1, 502, 106689528, 114483233476184, 24796191085864033165, 114483233476184, 106689528, 502, 1},
{1, 1013, 1144308880, 15719175021346280, 122840429081339181241876, 122840429081339181241876, 15719175021346280, 1144308880, 1013, 1},
{1, 2036, 11648950566, 1783118588818703136, 374703636611686539073985376, 8010652671072868708703768907910344, 374703636611686539073985376, 1783118588818703136, 11648950566, 2036, 1}

Mathematica

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

Crossrefs

Sequence in context: A285357 A174526 A008292 * A157221 A146967 A173152

Adjacent sequences: A174033 A174034 A174035 * A174037 A174038 A174039

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 06 2010

Status

approved