A174946 A symmetrical triangle sequence based on:q=2/12;t(n,m,q)=12*(Binomial[n, m]*(1 - q) + (((n + m + 1)!/(n + 1)!* m!) + ((2*n - m + 1)!/(n + 1)!*(n - m)!))*q)

1, 1, 1, 1, -55, 1, 1, -2371, -2371, 1, 1, -141079, -144767, -141079, 1, 1, -13063627, -13299239, -13299239, -13063627, 1, 1, -1756339135, -1778768213, -1779131331, -1778768213, -1756339135, 1, 1, -323805081523, -326881525841, -326918009541

Offset

0,5

Comments

Row sums are:

{1, 2, -53, -4740, -426923, -52725730, -8849346025, -1955209233808,

-552118682234375, -194345617889671998, -83514395998614084005,...}

Links

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

Formula

q=2/12;

t(n,m,q)=12*(Binomial[n, m]*(1 - q) + (((n + m + 1)!/(n + 1)!* m!) + ((2*n - m + 1)!/(n + 1)!*(n - m)!))*q);

out_n,m,q=t(n,m,q)-t(n,0,q)+1

Example

{1},
{1, 1},
{1, -55, 1},
{1, -2371, -2371, 1},
{1, -141079, -144767, -141079, 1},
{1, -13063627, -13299239, -13299239, -13063627, 1},
{1, -1756339135, -1778768213, -1779131331, -1778768213, -1756339135, 1},
{1, -323805081523, -326881525841, -326918009541, -326918009541, -326881525841, -323805081523, 1},
{1, -78460462079911, -79036461503291, -79041593014011, -79041649039951, -79041593014011, -79036461503291, -78460462079911, 1},
{1, -24186745110527899, -24328032061131923, -24329011779050579, -24329019994125599, -24329019994125599, -24329011779050579, -24328032061131923, -24186745110527899, 1},
{1, -9245027631071231887, -9289016465360485337, -9289260596277015803, -9289262200205068631, -9289262212786480691, -9289262200205068631, -9289260596277015803, -9289016465360485337, -9245027631071231887, 1}

Mathematica

t[n_, m_, q_] = 12*(Binomial[n, m]*(1 - q) + (((n + m + 1)!/(n + 1)!*m!) + ((2*n - m + 1)!/(n + 1)!*(n - m)!))*q);
Table[Flatten[Table[Table[t[ n, m, q] - t[n, 0, q] + 1, {m, 0, n}], {n, 0, 10}]], {q, 0, 1, 1/12}]

Crossrefs

Sequence in context: A363458 A218430 A159732 * A182119 A227856 A057965

Adjacent sequences: A174943 A174944 A174945 * A174947 A174948 A174949

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Apr 02 2010

Status

approved