A241186 Triangle read by rows: T(n,k) (0 <= k <= n) = numerator of Integral_{x=0..n} binomial(x,k).

0, 1, 1, 2, 2, 1, 3, 9, 9, 3, 4, 8, 20, 8, 14, 5, 25, 175, 75, 425, 95, 6, 18, 27, 24, 123, 33, 41, 7, 49, 539, 1225, 26117, 2499, 30919, 5257, 8, 32, 208, 96, 3928, 2336, 18128, 736, 3956, 9, 81, 405, 1323, 14661, 4455, 159219, 103437, 26649, 25713

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..54.

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. A241187, A100640, A100641.

Sequence in context: A113326 A262157 A090447 * A258222 A112324 A061531

Adjacent sequences: A241183 A241184 A241185 * A241187 A241188 A241189

Keyword

nonn,tabl,frac

Author

N. J. A. Sloane, Apr 24 2014

Status

approved