A174949 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, 5, 1, 1, -11, -11, 1, 1, -99, -119, -99, 1, 1, -451, -611, -611, -451, 1, 1, -1783, -2561, -2763, -2561, -1783, 1, 1, -6787, -10007, -11211, -11211, -10007, -6787, 1, 1, -25651, -38231, -43627, -45071, -43627, -38231, -25651, 1, 1, -97139

Offset

0,5

Comments

Row sums are:

{1, 2, 7, -20, -315, -2122, -11449, -56008, -260087, -1170710, -5163049,...}

Links

Table of n, a(n) for n=0..46.

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, 5, 1},
{1, -11, -11, 1},
{1, -99, -119, -99, 1},
{1, -451, -611, -611, -451, 1},
{1, -1783, -2561, -2763, -2561, -1783, 1},
{1, -6787, -10007, -11211, -11211, -10007, -6787, 1},
{1, -25651, -38231, -43627, -45071, -43627, -38231, -25651, 1},
{1, -97139, -145379, -167339, -175499, -175499, -167339, -145379, -97139, 1},
{1, -369399, -553673, -639867, -675861, -685451, -675861, -639867, -553673, -369399, 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: A296039 A296974 A146954 * A174861 A110522 A146987

Adjacent sequences: A174946 A174947 A174948 * A174950 A174951 A174952

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Apr 02 2010

Status

approved