A146532 Triangle read by rows: a(n)=2^Floor[n/2]*Gamma[1 + Floor[n/2]]; t(n,m) = a[n]/(a[n - m]*a[m]).

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 4, 2, 4, 1, 1, 1, 2, 2, 1, 1, 1, 6, 3, 12, 3, 6, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 8, 4, 24, 6, 24, 4, 8, 1, 1, 1, 4, 4, 6, 6, 4, 4, 1, 1, 1, 10, 5, 40, 10, 60, 10, 40, 5, 10, 1

Offset

0,5

Comments

The row sums are: {1, 2, 4, 4, 12, 8, 32, 16, 80, 32, 192}.

Links

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

Formula

a(n)=2^Floor[n/2]*Gamma[1 + Floor[n/2]]; t(n,m) = a[n]/(a[n - m]*a[m]).

Example

{1}, {1, 1}, {1, 2, 1}, {1, 1, 1, 1}, {1, 4, 2, 4, 1}, {1, 1, 2, 2, 1, 1}, {1, 6, 3, 12, 3, 6, 1}, {1, 1, 3, 3, 3, 3, 1, 1}, {1, 8, 4, 24, 6, 24, 4, 8, 1}, {1, 1, 4, 4, 6, 6, 4, 4, 1, 1}, {1, 10, 5, 40, 10, 60, 10, 40, 5, 10, 1}

Mathematica

Clear[a, n, t]; a[n_] = 2^Floor[n/2]*Gamma[1 + Floor[n/2]]; t[n_, m_] = a[n]/(a[n - m]*a[m]); Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Crossrefs

Sequence in context: A135303 A036065 A082907 * A305720 A225372 A184879

Adjacent sequences: A146529 A146530 A146531 * A146533 A146534 A146535

Keyword

nonn,tabl

Author

Roger L. Bagula, Oct 30 2008

Status

approved