A227027 Triangular numbers representable as x!/y! with y < x-1.

6, 120, 210, 990, 7140, 185136, 242556, 2162160, 8239770, 258474216, 279909630, 9508687656, 323015470680, 10973017315470, 372759573255306, 12662852473364940, 430164224521152660, 14612920781245825506, 496409142337836914550

Offset

1,1

Comments

Triangular numbers in A045619, except A045619(1)=0. The sequence is infinite because A029549 is a subsequence. According to Melissen's comment in A097571, y > x-7.

The sequence of x's producing a(n): A227026.

a(2) and a(3) have two representations:

a(2) = 120 = 5*4*3*2 = 6*5*4.

a(3) = 210 = 7*6*5 = 15*14.

Links

Table of n, a(n) for n=1..19.

Example

990 is in the sequence since 990 = 11!/8! = 11*10*9 is a ratio of factorials and 990 = (44)(44 + 1)/2 is a triangular number.

Crossrefs

Cf. A000217, A001219, A029549, A045619, A097571, A227026.

Sequence in context: A127726 A117063 A178911 * A001219 A224303 A076233

Adjacent sequences: A227024 A227025 A227026 * A227028 A227029 A227030

Keyword

nonn

Author

Alex Ratushnyak, Jun 27 2013

Status

approved