A174544 A mirrored symmetrical triangle of the Stirling numbers of the second kind.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 15, 15, 1, 1, 1, 1, 31, 90, 31, 1, 1, 1, 1, 63, 301, 301, 63, 1, 1, 1, 1, 127, 966, 1701, 966, 127, 1, 1, 1, 1, 255, 3025, 7770, 7770, 3025, 255, 1, 1, 1, 1, 511, 9330, 34105, 42525, 34105, 9330, 511, 1, 1

Offset

0,13

Comments

Row Sums are: 1, 2, 3, 4, 11, 34, 156, 732, 3891, 22104, 130421,...

Links

Table of n, a(n) for n=0..65.

Formula

T(n,0) = 1. T(n,k) = A008277(n,k) if 1<=k<=n/2. T(n,k) = T(n,n-k).

Example

1;
1, 1;
1, 1, 1;
1, 1, 1, 1;
1, 1, 7, 1, 1;
1, 1, 15, 15, 1, 1;
1, 1, 31, 90, 31, 1, 1;
1, 1, 63, 301, 301, 63, 1, 1;
1, 1, 127, 966, 1701, 966, 127, 1, 1;
1, 1, 255, 3025, 7770, 7770, 3025, 255, 1, 1;
1, 1, 511, 9330, 34105, 42525, 34105, 9330, 511, 1, 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: A284097 A091258 A351568 * A168423 A350071 A336844

Adjacent sequences: A174541 A174542 A174543 * A174545 A174546 A174547

Keyword

nonn,tabl

Author

Roger L. Bagula, Mar 22 2010

Extensions

Formula and NAME cleaned up by R. J. Mathar, Aug 28 2013

Status

approved