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A156811 Triangle read by rows: t(n,m)=If[BernoulliB[n - m] == 0, 0, Binomial[n, m]*BernoulliB[n - m]^(-m)]. 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, -2, 31, 186, 2091, 32750, -780961, 58054738, -3045496877, 153819074262,...}.

Steve Roman gives this function as one for the Stirling 2nd numbers,but

the results doesn't turn out right in Mathematica.

REFERENCES

Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page 99.

LINKS

Table of n, a(n) for n=0..56.

FORMULA

t(n,m)=If[BernoulliB[n - m] == 0, 0, Binomial[n, m]*BernoulliB[n - m]^(-m)].

EXAMPLE

{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}

MATHEMATICA

Clear[t, n, m];

t[n_, m_] = If[ BernoulliB[n - m] == 0, 0, Binomial[n, m]*BernoulliB[n - m]^(-m)];

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A007789 A081114 A069018 * A246609 A130636 A299354

Adjacent sequences:  A156808 A156809 A156810 * A156812 A156813 A156814

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 16 2009

STATUS

approved

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Last modified May 11 16:07 EDT 2021. Contains 343793 sequences. (Running on oeis4.)