A174148 A symmetrical binomial product triangle sequence:q=2; t(n,m,q)=If[n == 0 || n == 1, 1, Product[Binomial[n + i, m + i], {i, -Floor[q/2], Floor[q/2]}] + Product[Binomial[n + i, n - m + i], {i, -Floor[q/2], Floor[q/2]}]]

1, 1, 1, 1, 12, 1, 1, 42, 42, 1, 1, 100, 360, 100, 1, 1, 195, 1700, 1700, 195, 1, 1, 336, 5775, 14000, 5775, 336, 1, 1, 532, 15876, 75950, 75950, 15876, 532, 1, 1, 792, 37632, 312816, 617400, 312816, 37632, 792, 1, 1, 1125, 79920, 1058400, 3630312, 3630312

Offset

0,5

Comments

Row sums are:

1, 2, 14, 86, 562, 3792, 26224, 184718, 1319882, 9539516, 69594340,...

Links

Table of n, a(n) for n=0..50.

Formula

q=2;

t(n,m,q)=If[n == 0 || n == 1, 1, Product[Binomial[n + i, m + i], {i, -Floor[q/2], Floor[q/2]}] +

Product[Binomial[n + i, n - m + i], {i, -Floor[q/2], Floor[q/2]}]]

Example

{1},
{1, 1},
{1, 12, 1},
{1, 42, 42, 1},
{1, 100, 360, 100, 1},
{1, 195, 1700, 1700, 195, 1},
{1, 336, 5775, 14000, 5775, 336, 1},
{1, 532, 15876, 75950, 75950, 15876, 532, 1},
{1, 792, 37632, 312816, 617400, 312816, 37632, 792, 1},
{1, 1125, 79920, 1058400, 3630312, 3630312, 1058400, 79920, 1125, 1},
{1, 1540, 155925, 3088800, 16881480, 29338848, 16881480, 3088800, 155925, 1540, 1}

Mathematica

t[n_, m_, q_] = If[n == 0 || n == 1, 1, Product[Binomial[n + i, m + i], {i, - Floor[q/2], Floor[q/2]}] + Product[Binomial[n + i, n - m + i], { i, -Floor[q/2], Floor[q/2]}]];
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10, 2}]

Crossrefs

Sequence in context: A186432 A176489 A174039 * A155495 A157273 A350729

Adjacent sequences: A174145 A174146 A174147 * A174149 A174150 A174151

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 09 2010

Status

approved