A174187 A four product triangle sequence based on :a=2;f(n,a)=f(n - 1, a) + a*f(n - 2, a)

1, 1, 1, 1, 15, 1, 1, 165, 165, 1, 1, 3465, 38115, 3465, 1, 1, 49665, 11472615, 11472615, 49665, 1, 1, 844305, 2795493855, 58705370955, 2795493855, 844305, 1, 1, 13125105, 738772785135, 222370608325635, 222370608325635, 738772785135, 13125105, 1, 1

Offset

0,5

Comments

Row sums are:

{1, 2, 17, 332, 45047, 23044562, 64298047277, 446218788471752,

15586551283295860067, 1872235155190574164923902,

1140569746063885365760212575897,...}

Links

Table of n, a(n) for n=0..36.

Formula

a=2;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, 15, 1},
{1, 165, 165, 1},
{1, 3465, 38115, 3465, 1},
{1, 49665, 11472615, 11472615, 49665, 1},
{1, 844305, 2795493855, 58705370955, 2795493855, 844305, 1},
{1, 13125105, 738772785135, 222370608325635, 222370608325635, 738772785135, 13125105, 1},
{1, 213126705, 186487358761935, 954255814784821395, 13677666678582439995, 954255814784821395, 186487358761935, 213126705, 1},
{1, 3385245105, 48099075656401935, 3826093444807389812595, 932291436051400651002315, 932291436051400651002315, 3826093444807389812595, 48099075656401935, 3385245105, 1},
{1, 54363053745, 12268817438874211215, 15847349302992724519557555, 60028318491617986596036785835, 1020481414357505772132625359195, 60028318491617986596036785835, 15847349302992724519557555, 12268817438874211215, 54363053745, 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: A176226 A155493 A156939 * A174693 A340430 A022178

Adjacent sequences: A174184 A174185 A174186 * A174188 A174189 A174190

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 11 2010

Status

approved