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)]]

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, 252, 2408, 2408, 252, 2, 1, 1, 2, 508, 7728, 27216, 7728, 508, 2, 1, 1, 2, 1020, 24200, 124320, 124320, 24200, 1020, 2, 1, 1, 2, 2044, 74640, 545680, 1360800, 545680

Offset

0,5

Comments

Row Sums are:

{1, 2, 4, 6, 34, 126, 974, 5326, 43694, 299086, 2605534,...}

Links

Table of n, a(n) for n=0..61.

Formula

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)]]

Example

{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, 252, 2408, 2408, 252, 2, 1},
{1, 2, 508, 7728, 27216, 7728, 508, 2, 1},
{1, 2, 1020, 24200, 124320, 124320, 24200, 1020, 2, 1},
{1, 2, 2044, 74640, 545680, 1360800, 545680, 74640, 2044, 2, 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: A152719 A107044 A141591 * A102523 A323023 A083415

Adjacent sequences: A174542 A174543 A174544 * A174546 A174547 A174548

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 22 2010

Status

approved