A155583 The sequence is a factorization of a designed multi-bifurcative triangle sequence: t(n,m)=A155582(n,m); f(n, m) = If[m <= Floor[n/2], f(m, 1)*f(n - m, 1)*t(n, m)].

1, 1, 2, 6, 12, 28, 36, 36, 216, 216, 720, 1512, 1512, 2520, 12096, 12096, 12096, 10080, 60480, 108864, 108864, 54432, 604800, 604800, 1088640, 544320, 326592

Offset

0,3

Comments

Row sums are:

{1, 1, 2, 6, 40, 72, 1152, 5544, 46368, 332640, 3169152,...}.

Links

Table of n, a(n) for n=0..26.

Formula

t(n,m)=A155582(n,m); f(n, m) = If[m <= Floor[n/2], f(m, 1)*f(n - m, 1)*t(n, m)].

Example

Factor sequence is:
{1},
{1},
{2},
{6},
{12, 28},
{36, 36},
{216, 216, 720},
{1512, 1512, 2520},
{12096, 12096, 12096, 10080},
{60480, 108864, 108864, 54432}, {604800, 604800, 1088640, 544320, 326592}

Mathematica

Clear[t, a, b, c, n, m, f, x];
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]]]];
f[0, 1] = 1; f[1, 1] = 1; f[2, 1] = 2;
f[n_, m_] := f[n, m] = If[m <= Floor[n/2], f[m, 1]*f[n - m, 1]*t[n, m]];
a = Join[{{1}}, {{1}}, Table[Table[f[n, m], {m, 1, Floor[n/2]}], {n, 2, 10}]];
Flatten[%]

Crossrefs

Cf. A155582

Sequence in context: A356465 A166963 A188476 * A140853 A185961 A290674

Adjacent sequences: A155580 A155581 A155582 * A155584 A155585 A155586

Keyword

nonn,uned

Author

Roger L. Bagula, Jan 24 2009

Status

approved