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

0,7

Links

Table of n, a(n) for n=0..37.

Eric Weisstein's World of Mathematics, Tetrahedral Number

Index to sequences related to pyramidal numbers

Index entries for sequences related to partitions

Formula

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

Example

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

Crossrefs

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

Sequence in context: A140600 A056396 A085043 * A143818 A238879 A286258

Adjacent sequences: A338583 A338584 A338585 * A338587 A338588 A338589

Keyword

nonn,changed

Author

Ilya Gutkovskiy, Nov 08 2020

Status

approved