A077168 Lexicographically earliest infinite sequence of distinct positive numbers with the property that when written as a triangle, the product of each row is a factorial.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 259200, 15, 16, 17, 18, 19, 87178291200, 20, 21, 22, 23, 24, 25, 202741834014720, 26, 27, 28, 29, 30, 31, 32, 484725313854093312000000, 33, 34, 35, 36, 37, 38, 39, 40, 4438779300500903005519872000000, 41, 42, 43, 44

Offset

0,2

Comments

The old definition was "Triangle formed by grouping the natural numbers so that the n-th group contains n numbers whose product is a factorial.". - N. J. A. Sloane, Oct 06 2024

Links

Table of n, a(n) for n=0..48.

Example

Triangle begins:
1,
2, 3,
4, 5, 6,
7, 8, 9, 10,
11, 12, 13, 14, 259200,
15, 16, 17, 18, 19, 87178291200,
20, 21, 22, 23, 24, 25, 202741834014720,
26, 27, 28, 29, 30, 31, 32, 484725313854093312000000,
33, 34, 35, 36, 37, 38, 39, 40, 4438779300500903005519872000000,
...
The row products are:
 1 = 1!
 2*3 = 6 = 3!
 4*5*6 = 120 = 5!
 7*8*9*10 = 5040 = 7!
 11*12*13*14*259200 = 6227020800 = 13!
 15*16*17*18*19*87178291200 = 121645100408832000 = 19!
 20*21*22*23*24*25*202741834014720 = 25852016738884976640000 = 23!
 26*27*28*29*30*31*32*484725313854093312000000 = 8222838654177922817725562880000000 = 31!
 33*34*35*36*37*38*39*40*4438779300500903005519872000000 = 37!
 ...

Crossrefs

Cf. A077169, A077170, A077171.

Sequence in context: A044916 A065672 A065673 * A195099 A195098 A102452

Adjacent sequences: A077165 A077166 A077167 * A077169 A077170 A077171

Keyword

nonn,tabl

Author

Amarnath Murthy, Nov 01 2002

Extensions

More terms from Sascha Kurz, Feb 10 2003

Entry revised by N. J. A. Sloane, Oct 06 2024

Status

approved