A338778 Number of ordered ways of writing n-th tetrahedral number as a sum of n positive tetrahedral numbers.

1, 1, 0, 0, 0, 20, 195, 1890, 6286, 94584, 1065120, 12345432, 194450586, 2844976135, 44569913570, 740023110855, 13144353701940, 241663182769494, 4707408836458200, 95865898167054186, 2038122531703155798, 45103282424247100962, 1037559653596650520776, 24776005985596646165127

Offset

0,6

Links

Table of n, a(n) for n=0..23.

Eric Weisstein's World of Mathematics, Tetrahedral Number

Index to sequences related to pyramidal numbers

Index entries for sequences related to compositions

Formula

a(n) = [x^A000292(n)] (Sum_{j>=1} x^A000292(j))^n.

Example

The 5th tetrahedral number is 35 and 35 = 1 + 4 + 10 + 10 + 10 (20 permutations), so a(5) = 20.

Crossrefs

Cf. A000292, A298269, A298672, A298857, A298858, A303170, A338586.

Sequence in context: A219369 A245137 A232224 * A343242 A219935 A191299

Adjacent sequences: A338775 A338776 A338777 * A338779 A338780 A338781

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 08 2020

Status

approved