login
A096078
Triangle read by rows: T(n,k) = (k+1)T(n-1,k) + (n-k+1)T(n,k-1).
0
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
0,5
LINKS
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).
EXAMPLE
Table begins:
1
1 1
1 4 4
1 11 34 34
1 26 180 496 496
1 57 768 4288 11056 11056
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_] := (j + 1)T[n - 1, j] + (n - j + 1)T[n, j - 1]); Flatten[ Table[ T[n, k], {n, 0, 8}, {k, 0, n}]] (* Robert G. Wilson v, Jul 23 2004 *)
CROSSREFS
Sequence in context: A360707 A365674 A106026 * A140313 A102323 A145902
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Boddington, Jul 22 2004
EXTENSIONS
Edited and extended by Robert G. Wilson v, Jul 23 2004
STATUS
approved