A174186 A four product triangle sequence based on :a=1;f(n,a)=f(n - 1, a) + a*f(n - 2, a)

1, 1, 1, 1, 6, 1, 1, 30, 30, 1, 1, 240, 1200, 240, 1, 1, 1560, 62400, 62400, 1560, 1, 1, 10920, 2839200, 22713600, 2839200, 10920, 1, 1, 74256, 135145920, 7027587840, 7027587840, 135145920, 74256, 1, 1, 510510, 6318071760, 2299778120640

Offset

0,5

Comments

Row sums are:

{1, 2, 8, 62, 1682, 127922, 28413842, 14325616034, 19560751189982,

68454330820638842, 661989975165467768162,...}

Links

Table of n, a(n) for n=0..39.

Formula

a=1;f(n,a)=f(n - 1, a) + a*f(n - 2, a);

c(n,a)=If[n == 0 || n == 1, 1, Product[f(i - 1, a)*f(i, a)*f(i + 1, a)*f(i + 2, a), {i, 2, n}]];

t(n,m,a)=c(n,a)/(c(m,a)*c(n-m,a))

Example

{1},
{1, 1},
{1, 6, 1},
{1, 30, 30, 1},
{1, 240, 1200, 240, 1},
{1, 1560, 62400, 62400, 1560, 1},
{1, 10920, 2839200, 22713600, 2839200, 10920, 1},
{1, 74256, 135145920, 7027587840, 7027587840, 135145920, 74256, 1},
{1, 510510, 6318071760, 2299778120640, 14948557784160, 2299778120640, 6318071760, 510510, 1},
{1, 3495030, 297374627550, 736061678111760, 33490806354085080, 33490806354085080, 736061678111760, 297374627550, 3495030, 1},
{1, 23965920, 13960268229600, 237561884463103200, 73501647052884130080, 514511529370188910560, 73501647052884130080, 237561884463103200, 13960268229600, 23965920, 1}

Mathematica

f[0, a_] := 0; f[1, a_] := 1;
f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a];
c[n_, a_] := If[n == 0 || n == 1, 1, Product[f[i - 1, a]*f[i, a]*f[i + 1, a]*f[i + 2, a], {i, 2, n}]]; Q w[n_, m_, q_] := c[n, q]/(c[m, q]*c[n - m, q]);
Table[Flatten[Table[Table[w[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 1, 12}]

Crossrefs

Sequence in context: A340475 A368848 A265603 * A111578 A166349 A176429

Adjacent sequences: A174183 A174184 A174185 * A174187 A174188 A174189

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 11 2010

Status

approved