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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, 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 (list; table; graph; refs; listen; history; text; internal format)
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 A130636 A299354

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

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Last modified May 22 06:54 EDT 2022. Contains 353933 sequences. (Running on oeis4.)