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)]]

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, 1, 3, 567, 8127, 8127, 567, 3, 1, 1, 3, 1143, 26082, 137781, 26082, 1143, 3, 1, 1, 3, 2295, 81675, 629370, 629370, 81675, 2295, 3, 1, 1, 3, 4599, 251910, 2762505, 10333575

Offset

0,5

Comments

Row Sums are:

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

Links

Table of n, a(n) for n=0..60.

Formula

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)]]

Example

{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},
{1, 3, 567, 8127, 8127, 567, 3, 1},
{1, 3, 1143, 26082, 137781, 26082, 1143, 3, 1},
{1, 3, 2295, 81675, 629370, 629370, 81675, 2295, 3, 1},
{1, 3, 4599, 251910, 2762505, 10333575, 2762505, 251910, 4599, 3, 1}

Mathematica

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

Crossrefs

Sequence in context: A143086 A327481 A152714 * A134444 A176149 A091442

Adjacent sequences: A174543 A174544 A174545 * A174547 A174548 A174549

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 22 2010

Status

approved