login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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]}]] 0
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 (list; table; graph; refs; listen; history; text; internal format)
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 A168518

Adjacent sequences:  A174145 A174146 A174147 * A174149 A174150 A174151

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 09 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 23 18:51 EDT 2020. Contains 337315 sequences. (Running on oeis4.)