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%I #4 Nov 08 2020 23:13:58
%S 1,1,0,0,0,20,195,1890,6286,94584,1065120,12345432,194450586,
%T 2844976135,44569913570,740023110855,13144353701940,241663182769494,
%U 4707408836458200,95865898167054186,2038122531703155798,45103282424247100962,1037559653596650520776,24776005985596646165127
%N Number of ordered ways of writing n-th tetrahedral number as a sum of n positive tetrahedral numbers.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>
%H <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F a(n) = [x^A000292(n)] (Sum_{j>=1} x^A000292(j))^n.
%e The 5th tetrahedral number is 35 and 35 = 1 + 4 + 10 + 10 + 10 (20 permutations), so a(5) = 20.
%Y Cf. A000292, A298269, A298672, A298857, A298858, A303170, A338586.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Nov 08 2020
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