A174640 Triangle read by rows: T(n,k) = A033306(n,k) - A033306(n,0) + 1.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 6, 10, 6, 1, 1, 24, 49, 49, 24, 1, 1, 110, 248, 298, 248, 110, 1, 1, 545, 1308, 1749, 1749, 1308, 545, 1, 1, 2877, 7229, 10421, 11611, 10421, 7229, 2877, 1, 1, 16114, 41998, 64114, 77134, 77134, 64114, 41998, 16114, 1, 1, 95496

Offset

0,8

References

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 80.

Links

Table of n, a(n) for n=0..56.

Example

Triangle begins:
  {1},
  {1, 1},
  {1, 1, 1},
  {1, 2, 2, 1},
  {1, 6, 10, 6, 1},
  {1, 24, 49, 49, 24, 1},
  {1, 110, 248, 298, 248, 110, 1},
  {1, 545, 1308, 1749, 1749, 1308, 545, 1},
  ...

Mathematica

b[0] := 1;
b[n_] := b[n] = Total[Table[b[k]Binomial[n - 1, k], {k, 0, n - 1}]];
a = b /@ Range[0, 70];
t[n_, m_] := Binomial[n, m]*a[[m + 1]]*a[[n - m + 1]];
Table[Table[t[n, m] - t[n, 0] + 1, {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Cf. A033306.

Sequence in context: A263755 A135879 A176224 * A138169 A139331 A173886

Adjacent sequences: A174637 A174638 A174639 * A174641 A174642 A174643

Keyword

nonn,tabl,less

Author

Roger L. Bagula, Mar 25 2010

Extensions

Edited by Sean A. Irvine, Mar 01 2026

Status

approved