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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]]] 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 18 11:56 EDT 2018. Contains 316321 sequences. (Running on oeis4.)