A338586 Number of partitions of the n-th tetrahedral number into exactly n positive tetrahedral numbers.

1, 1, 0, 0, 0, 1, 2, 5, 5, 20, 35, 75, 154, 336, 730, 1570, 3394, 7339, 16085, 35015, 76269, 164821, 359704, 782004, 1696804, 3668860, 7953962, 17184203, 37093184, 79825297, 171824175, 368838299, 790404448, 1690297309, 3610816466, 7696144659, 16374004711, 34766160358

Offset: 0

Author

Ilya Gutkovskiy, Nov 08 2020

Keywords

• nonn

Examples

			The 6th tetrahedral number is 56 and 56 = 1 + 1 + 4 + 10 + 20 + 20 = 4 + 4 + 4 + 4 + 20 + 20, so a(6) = 2.
		

Links

• Eric Weisstein's World of Mathematics, Tetrahedral Number
• Index to sequences related to pyramidal numbers
• Index entries for sequences related to partitions

Crossrefs

Cf. A000292, A068980, A298269, A298857, A303170, A307643, A338585, A338778.

Formula

a(n) = [x^A000292(n) y^n] Product_{j>=1} 1 / (1 - y*x^A000292(j)).