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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

%I

%S 1,1,1,1,4,1,1,11,11,1,1,26,2145,26,1,1,57,45451,45451,57,1,1,120,

%T 708645,2347470160,708645,120,1,1,247,9212778,634928765569,

%U 634928765569,9212778,247,1,1,502,106689528,114483233476184,24796191085864033165

%N 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]]]

%C Row Sums are:

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

%C 245680889601030693796100, 8010653420480145498314047991192574,...}.

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

%e {1},

%e {1, 1},

%e {1, 4, 1},

%e {1, 11, 11, 1},

%e {1, 26, 2145, 26, 1},

%e {1, 57, 45451, 45451, 57, 1},

%e {1, 120, 708645, 2347470160, 708645, 120, 1},

%e {1, 247, 9212778, 634928765569, 634928765569, 9212778, 247, 1},

%e {1, 502, 106689528, 114483233476184, 24796191085864033165, 114483233476184, 106689528, 502, 1},

%e {1, 1013, 1144308880, 15719175021346280, 122840429081339181241876, 122840429081339181241876, 15719175021346280, 1144308880, 1013, 1},

%e {1, 2036, 11648950566, 1783118588818703136, 374703636611686539073985376, 8010652671072868708703768907910344, 374703636611686539073985376, 1783118588818703136, 11648950566, 2036, 1}

%t << DiscreteMath`Combinatorica`

%t 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}];

%t Flatten[%]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Mar 06 2010

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Last modified August 4 19:28 EDT 2020. Contains 336202 sequences. (Running on oeis4.)