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A174545 A symmetrical triangle based on Stirling numbers of the second kind :q=2;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 1,1,1,1,2,1,1,2,2,1,1,2,28,2,1,1,2,60,60,2,1,1,2,124,720,124,2,1,1,2,

%T 252,2408,2408,252,2,1,1,2,508,7728,27216,7728,508,2,1,1,2,1020,24200,

%U 124320,124320,24200,1020,2,1,1,2,2044,74640,545680,1360800,545680

%N A symmetrical triangle based on Stirling numbers of the second kind :q=2;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, 4, 6, 34, 126, 974, 5326, 43694, 299086, 2605534,...}

%F q=2;

%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, 2, 1},

%e {1, 2, 2, 1},

%e {1, 2, 28, 2, 1},

%e {1, 2, 60, 60, 2, 1},

%e {1, 2, 124, 720, 124, 2, 1},

%e {1, 2, 252, 2408, 2408, 252, 2, 1},

%e {1, 2, 508, 7728, 27216, 7728, 508, 2, 1},

%e {1, 2, 1020, 24200, 124320, 124320, 24200, 1020, 2, 1},

%e {1, 2, 2044, 74640, 545680, 1360800, 545680, 74640, 2044, 2, 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 September 19 18:36 EDT 2021. Contains 347564 sequences. (Running on oeis4.)