A241187 - OEIS

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A241187 - OEIS

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A241187

Triangle read by rows: T(n,k) (0 <= k <= n) = denominator of Integral_{x=0..n} binomial(x,k).

1

1, 1, 2, 1, 1, 3, 1, 2, 4, 8, 1, 1, 3, 3, 45, 1, 2, 12, 8, 144, 288, 1, 1, 1, 1, 10, 10, 140, 1, 2, 12, 24, 720, 160, 8640, 17280, 1, 1, 3, 1, 45, 45, 945, 189, 14175, 1, 2, 4, 8, 80, 32, 2240, 4480, 6400, 89600, 1, 1, 3, 3, 18, 2, 756, 189, 4536, 4536, 299376

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

OFFSET

0,3

COMMENTS

Suggested by the integral formula for the Cotesian numbers A100640/A100641.

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

Triangle of fractions Integral_{x=0..n} binomial(x,k) begins:

[0],

[1, 1/2],

[2, 2, 1/3],

[3, 9/2, 9/4, 3/8],

[4, 8, 20/3, 8/3, 14/45],

[5, 25/2, 175/12, 75/8, 425/144, 95/288],

[6, 18, 27, 24, 123/10, 33/10, 41/140],

[7, 49/2, 539/12, 1225/24, 26117/720, 2499/160, 30919/8640, 5257/17280],

[8, 32, 208/3, 96, 3928/45, 2336/45, 18128/945, 736/189, 3956/14175],

...

MAPLE

T:=proc(n, k) integrate( expand(binomial(x, k)), x=0..n); end;

t0:=[seq( [seq(T(n, k), k=0..n)], n=0..10)];

CROSSREFS

Cf. A241186, A100640, A100641.

Sequence in context: A238899 A187207 A050117 * A212822 A309041 A249143

Adjacent sequences: A241184 A241185 A241186 * A241188 A241189 A241190

KEYWORD

nonn,tabl,frac

AUTHOR

N. J. A. Sloane, Apr 24 2014

STATUS

approved