A096078 - OEIS

%I #11 Jun 27 2018 18:39:43

%S 1,1,1,1,4,4,1,11,34,34,1,26,180,496,496,1,57,768,4288,11056,11056,1,

%T 120,2904,28768,141584,349504,349504,1,247,10194,166042,1372088,

%U 6213288,14873104,14873104,1,502,34096,868744,11204160,82096368,350400832

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

%H Paul Barry, <a href="https://arxiv.org/abs/1803.06408">Three Études on a sequence transformation pipeline</a>, arXiv:1803.06408 [math.CO], 2018.

%F 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).

%e Table begins:

%e 1

%e 1 1

%e 1 4 4

%e 1 11 34 34

%e 1 26 180 496 496

%e 1 57 768 4288 11056 11056

%t 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 *)

%Y Cf. A000295, A002105.

%K easy,nonn,tabl

%O 0,5

%A _Paul Boddington_, Jul 22 2004

%E Edited and extended by _Robert G. Wilson v_, Jul 23 2004