A174667 Triangle read by rows: T(n, k) = A154692(n, k) - A154692(n, 0) + 1.

1, 1, 1, 1, 12, 1, 1, 56, 56, 1, 1, 216, 336, 216, 1, 1, 776, 1526, 1526, 776, 1, 1, 2700, 6228, 7848, 6228, 2700, 1, 1, 9236, 24146, 35486, 35486, 24146, 9236, 1, 1, 31248, 90960, 150432, 174624, 150432, 90960, 31248, 1, 1, 104816, 336206, 614846, 796286

Offset

0,5

Links

Table of n, a(n) for n=0..49.

Example

Triangle begins:
  {1},
  {1, 1},
  {1, 12, 1},
  {1, 56, 56, 1},
  {1, 216, 336, 216, 1},
  {1, 776, 1526, 1526, 776, 1},
  {1, 2700, 6228, 7848, 6228, 2700, 1},
  ...

Mathematica

a = 2; b = 3;
t[n_, m_] = (a^m*b^(n - m) + b^m*a^(n - m))*Binomial[n, m];
Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A154692.

Sequence in context: A157273 A350729 A168518 * A174672 A174151 A342890

Adjacent sequences: A174664 A174665 A174666 * A174668 A174669 A174670

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Mar 26 2010

Extensions

Edited by Sean A. Irvine, Mar 08 2026

Status

approved