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

Author

Ilya Gutkovskiy, Nov 08 2020

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Formula

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