A155582 See Mathematica program for definition.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 7, 2, 1, 1, 3, 3, 3, 3, 1, 1, 6, 9, 20, 9, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 5, 36, 84, 126, 126, 84, 36, 5, 1, 1, 10, 25, 120, 210, 252, 210, 120, 25, 10, 1

Offset

0,5

Links

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

Example

{1},
{1,  1},
{1,  2,  1},
{1,  3,  3,   1},
{1,  2,  7,   2,   1},
{1,  3,  3,   3,   3,   1},
{1,  6,  9,  20,   9,   6,   1},
{1,  7, 21,  35,  35,  21,   7,   1},
{1,  8, 28,  56,  70,  56,  28,   8,  1},
{1,  5, 36,  84, 126, 126,  84,  36,  5,  1},
{1, 10, 25, 120, 210, 252, 210, 120, 25, 10, 1}

Mathematica

a[0] = 1;
a[n_] := a[n] = ((4*n - 2)/(n + 1))*a[n - 1];
b[0] = 1;
b[n_] := b[n] = If[IntegerQ[((3*n - 2)/(n + 1))*b[n - 1]], ((3*n - 2)/(n + 1))*b[n - 1], If[IntegerQ[((4*n - 2)/( n + 1))*b[n - 1]], ((4*n - 2)/(n + 1))*b[n - 1], n*b[n - 1]]];
c[0] = 1;
c[n_] := c[n] = If[IntegerQ[((6*n - 4)/(n + 1))*c[n - 1]], ((6*n - 4)/(n + 1))*c[n - 1], If[IntegerQ[((4*n - 2)/(n + 1))*c[n - 1]], ((4*n - 2)/(n + 1))*c[n - 1], n*c[n - 1]]];
t[n_, m_] := t[n, m] = If[IntegerQ[a[n]/(a[m]*a[n - m])], a[n]/(a[m]*a[n - m]), If[IntegerQ[b[ n]/(b[m]*b[n - m])], b[n]/(b[m]* b[n - m]), If[IntegerQ[ c[n]/(c[m]*c[n - m])], c[n]/(c[m]*c[n - m]), Binomial[n, m]]]];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A204087 A080381 A080396 * A169946 A160832 A351522

Adjacent sequences: A155579 A155580 A155581 * A155583 A155584 A155585

Keyword

nonn,uned

Author

Roger L. Bagula, Jan 24 2009

Status

approved