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A174149 A symmetrical binomial product triangle sequence:q=4; 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, 0, 1, 1, 120, 120, 1, 1, 720, 5400, 720, 1, 1, 2520, 84700, 84700, 2520, 1, 1, 6720, 712950, 3136000, 712950, 6720, 1, 1, 15120, 4064256, 56080500, 56080500, 4064256, 15120, 1, 1, 30240, 17745840, 619178112, 1944810000, 619178112 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

1, 2, 2, 242, 6842, 174442, 4575342, 120319754, 3218718386, 87130425890,

2387489480048,...

LINKS

Table of n, a(n) for n=0..41.

FORMULA

q=4;

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, 0, 1},

{1, 120, 120, 1},

{1, 720, 5400, 720, 1},

{1, 2520, 84700, 84700, 2520, 1},

{1, 6720, 712950, 3136000, 712950, 6720, 1},

{1, 15120, 4064256, 56080500, 56080500, 4064256, 15120, 1},

{1, 30240, 17745840, 619178112, 1944810000, 619178112, 17745840, 30240, 1},

{1, 55440, 63795600, 4857209280, 38644152624, 38644152624, 4857209280, 63795600, 55440, 1},

{1, 95040, 197735175, 29523225600, 513405390960, 1301236586496, 513405390960, 29523225600, 197735175, 95040, 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: A051727 A174867 A244950 * A268920 A056466 A056456

Adjacent sequences:  A174146 A174147 A174148 * A174150 A174151 A174152

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 09 2010

STATUS

approved

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Last modified November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)