A174188 A four product triangle sequence based on :a=3;f(n,a)=f(n - 1, a) + a*f(n - 2, a)

1, 1, 1, 1, 28, 1, 1, 532, 532, 1, 1, 21280, 404320, 21280, 1, 1, 516040, 392190400, 392190400, 516040, 1, 1, 15997240, 294829133200, 11793165328000, 294829133200, 15997240, 1, 1, 427715680, 244366799454400, 237035795470768000

Offset

0,5

Comments

Row sums are:

{1, 2, 30, 1066, 446882, 785412882, 12382855588882, 474560325395876162,

149430618145736091033018, 183642180080454590264125715410,

1840703499938423522875527863428804802,...}

Links

Table of n, a(n) for n=0..31.

Formula

a=3;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, 28, 1},
{1, 532, 532, 1},
{1, 21280, 404320, 21280, 1},
{1, 516040, 392190400, 392190400, 516040, 1},
{1, 15997240, 294829133200, 11793165328000, 294829133200, 15997240, 1},
{1, 427715680, 244366799454400, 237035795470768000, 237035795470768000, 244366799454400, 427715680, 1},
{1, 12393061828, 189310959537323680, 5692580553287323057600, 138045078417217584146800, 5692580553287323057600, 189310959537323680, 12393061828, 1},
{1, 342789534892, 151721853568139975092, 121980856710070330416650080, 91699109031795370890716697640, 91699109031795370890716697640, 121980856710070330416650080, 151721853568139975092, 342789534892, 1},
{1, 9730799700160, 119129153690894980642240, 2775140915805593789011547872960, 55778725747162231920622684508253760, 1729140498162029189539303219755866560, 55778725747162231920622684508253760, 2775140915805593789011547872960, 119129153690894980642240, 9730799700160, 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: A347162 A347174 A352031 * A176641 A040796 A040797

Adjacent sequences: A174185 A174186 A174187 * A174189 A174190 A174191

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 11 2010

Status

approved