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

Author

Amarnath Murthy, Nov 01 2002

Keywords

• nonn
• tabl

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

Examples

			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. A076031, A077169, A077170, A077171.

Extensions

More terms from Sascha Kurz, Feb 10 2003

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