A174949 Triangle read by rows: T(n,k) = B(n,k) - B(n,0) + 1 where B(n,k) = 2 * (5*binomial(n,k)*(n+1)!*k!*(n-k)! + (n+k+1)!*(n-k)! + (2*n-k+1)!*k!) / ((n+1)!*k!*(n-k)!).

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

Offset

0,5

Comments

Triangle is symmetric.

Links

Table of n, a(n) for n=0..44.

Example

Triangle begins:
  {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},
  ...

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,less

Author

Roger L. Bagula, Apr 02 2010

Extensions

Edited by Sean A. Irvine, Mar 16 2026

Status

approved