A156811 Triangle T(n, k) = 0 if BernoulliB(n-k) = 0 otherwise round( binomial(n, k)/BernoulliB(n-k)^k ), read by rows.

1, 1, 1, 1, -4, 1, 0, 18, 12, 1, 1, 0, 216, -32, 1, 0, -150, 0, 2160, 80, 1, 1, 0, 13500, 0, 19440, -192, 1, 0, 294, 0, -945000, 0, 163296, 448, 1, 1, 0, 49392, 0, 56700000, 0, 1306368, -1024, 1, 0, -270, 0, 6223392, 0, -3061800000, 0, 10077696, 2304, 1, 1, 0, 40500, 0, 653456160, 0, 153090000000, 0, 75582720, -5120, 1

Offset

0,5

Links

G. C. Greubel, Table of n, a(n) for n = 0..1325

Formula

T(n, k) = 0 if BernoulliB(n-k) = 0 otherwise round( binomial(n, k)/BernoulliB(n-k)^k ).

Example

Triangle begins as:
  1;
  1,    1;
  1,   -4,     1;
  0,   18,    12,       1;
  1,    0,   216,     -32,         1;
  0, -150,     0,    2160,        80,           1;
  1,    0, 13500,       0,     19440,        -192,       1;
  0,  294,     0, -945000,         0,      163296,     448,        1;
  1,    0, 49392,       0,  56700000,           0, 1306368,    -1024,    1;
  0, -270,     0, 6223392,         0, -3061800000,       0, 10077696, 2304, 1;

Mathematica

T[n_, k_]:= If[BernoulliB[n-k]==0, 0, Round[Binomial[n, k]*BernoulliB[n-k]^(-k)]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten

Prog

(Magma)
A156811:= func< n, k | Bernoulli(n-k) eq 0 select 0 else Round( Binomial(n, k)/Bernoulli(n-k)^k ) >;
[A156811(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 10 2021
(Sage)
def A156811(n, k): return 0 if (bernoulli(n-k)==0) else round( binomial(n, k)/bernoulli(n-k)^k )
flatten([[A156811(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 10 2021

Crossrefs

Sequence in context: A345393 A081114 A069018 * A246609 A371080 A130636

Adjacent sequences: A156808 A156809 A156810 * A156812 A156813 A156814

Keyword

sign,tabl,less

Author

Roger L. Bagula, Feb 16 2009

Extensions

Definition corrected and edited by G. C. Greubel, Jun 10 2021

Status

approved