A156811 - OEIS

%I #10 Sep 08 2022 08:45:41

%S 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,

%T 19440,-192,1,0,294,0,-945000,0,163296,448,1,1,0,49392,0,56700000,0,

%U 1306368,-1024,1,0,-270,0,6223392,0,-3061800000,0,10077696,2304,1,1,0,40500,0,653456160,0,153090000000,0,75582720,-5120,1

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

%H G. C. Greubel, <a href="/A156811/b156811.txt">Table of n, a(n) for n = 0..1325</a>

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

%e Triangle begins as:

%e   1;

%e   1,    1;

%e   1,   -4,     1;

%e   0,   18,    12,       1;

%e   1,    0,   216,     -32,         1;

%e   0, -150,     0,    2160,        80,           1;

%e   1,    0, 13500,       0,     19440,        -192,       1;

%e   0,  294,     0, -945000,         0,      163296,     448,        1;

%e   1,    0, 49392,       0,  56700000,           0, 1306368,    -1024,    1;

%e   0, -270,     0, 6223392,         0, -3061800000,       0, 10077696, 2304, 1;

%t T[n_, k_]:= If[BernoulliB[n-k]==0, 0, Round[Binomial[n, k]*BernoulliB[n-k]^(-k)]];

%t Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten

%o (Magma)

%o A156811:= func< n,k | Bernoulli(n-k) eq 0 select 0 else Round( Binomial(n,k)/Bernoulli(n-k)^k ) >;

%o [A156811(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, Jun 10 2021

%o (Sage)

%o def A156811(n,k): return 0 if (bernoulli(n-k)==0) else round( binomial(n,k)/bernoulli(n-k)^k )

%o flatten([[A156811(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Jun 10 2021

%K sign,tabl,less

%O 0,5

%A _Roger L. Bagula_, Feb 16 2009

%E Definition corrected and edited by _G. C. Greubel_, Jun 10 2021