A096078 Triangle read by rows: T(n,k) = (k+1)*T(n-1,k) + (n-k+1)*T(n,k-1).

1, 1, 1, 1, 4, 4, 1, 11, 34, 34, 1, 26, 180, 496, 496, 1, 57, 768, 4288, 11056, 11056, 1, 120, 2904, 28768, 141584, 349504, 349504, 1, 247, 10194, 166042, 1372088, 6213288, 14873104, 14873104, 1, 502, 34096, 868744, 11204160, 82096368, 350400832

Offset: 0

Author

Paul Boddington, Jul 22 2004

Keywords

• easy
• nonn
• tabl

Examples

			Table begins:
  1
  1 1
  1 4 4
  1 11 34 34
  1 26 180 496 496
  1 57 768 4288 11056 11056
		

Links

• Paul Barry, Three Études on a sequence transformation pipeline, arXiv:1803.06408 [math.CO], 2018.

Crossrefs

Cf. A000295, A002105.

Programs

Mathematica

T[n_, 0] := 1; T[n_, 1] := 2^(n+1) - n - 2; T[n_, n_] := 2^(n+1)*(2^(2n+2) - 1)*Abs[ BernoulliB[2n + 2]]/ (n + 1); T[n_, k_] := (k + 1)T[n - 1, k] + (n - k + 1)T[n, k - 1]; Flatten[ Table[ T[n, k], {n, 0, 8}, {k, 0, n}]] (* Robert G. Wilson v, Jul 23 2004 *)

Formula

T(n-1, 1) given by Eulerian numbers, 2^n - n - 1 (A000295). T(n-1, n-1) given by 2^n*(2^{2n} - 1)*|B_{2n}|/n, B_n = Bernoulli numbers (A002105).

Extensions

Edited and extended by Robert G. Wilson v, Jul 23 2004