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 A174546 A symmetrical triangle based on Stirling numbers of the second kind :q=3;t(n,m,q)=If[m == 0 Or m == n, 1, If[Floor[n/2] greater than or equal to m, StirlingS2[ n, m]*q^m, StirlingS2[n, n - m]*q^(n - m)]] 0

%I

%S 1,1,1,1,3,1,1,3,3,1,1,3,63,3,1,1,3,135,135,3,1,1,3,279,2430,279,3,1,

%T 1,3,567,8127,8127,567,3,1,1,3,1143,26082,137781,26082,1143,3,1,1,3,

%U 2295,81675,629370,629370,81675,2295,3,1,1,3,4599,251910,2762505,10333575

%N A symmetrical triangle based on Stirling numbers of the second kind :q=3;t(n,m,q)=If[m == 0 Or m == n, 1, If[Floor[n/2] greater than or equal to m, StirlingS2[ n, m]*q^m, StirlingS2[n, n - m]*q^(n - m)]]

%C Row Sums are:

%C {1, 2, 5, 8, 71, 278, 2996, 17396, 192239, 1426688, 16371611,...}

%F q=3;

%F t(n,m,q)=If[m == 0 Or m == n, 1, If[Floor[n/2] greater than or equal to m, StirlingS2[ n, m]*q^m, StirlingS2[n, n - m]*q^(n - m)]]

%e {1},

%e {1, 1},

%e {1, 3, 1},

%e {1, 3, 3, 1},

%e {1, 3, 63, 3, 1},

%e {1, 3, 135, 135, 3, 1},

%e {1, 3, 279, 2430, 279, 3, 1},

%e {1, 3, 567, 8127, 8127, 567, 3, 1},

%e {1, 3, 1143, 26082, 137781, 26082, 1143, 3, 1},

%e {1, 3, 2295, 81675, 629370, 629370, 81675, 2295, 3, 1},

%e {1, 3, 4599, 251910, 2762505, 10333575, 2762505, 251910, 4599, 3, 1}

%t t[n_, m_, q_] = If[m == 0 || m == n, 1, If[Floor[n/2] >= m, StirlingS2[n, m]*q^ m, StirlingS2[n, n - m]*q^(n - m)]];

%t Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 10}]

%K nonn,tabl,uned

%O 0,5

%A _Roger L. Bagula_, Mar 22 2010

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Last modified July 24 00:28 EDT 2021. Contains 346265 sequences. (Running on oeis4.)