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A298857 Number of partitions of the n-th tetrahedral number into distinct tetrahedral numbers.

%I A298857 #5 Feb 16 2025 08:33:53
%S A298857 1,1,1,1,1,2,2,1,2,3,2,5,5,10,12,17,15,22,30,56,65,72,92,172,219,299,
%T A298857 368,478,810,1055,1508,1778,2277,3815,5214,7103,8615,11614,18079,
%U A298857 24428,33704,42877,56639,85597,116984,159179,199356,268965,400612,545674,740356,950897,1261597,1842307
%N A298857 Number of partitions of the n-th tetrahedral number into distinct tetrahedral numbers.
%H A298857 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>
%H A298857 <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%H A298857 <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F A298857 a(n) = [x^A000292(n)] Product_{k>=1} (1 + x^A000292(k)).
%F A298857 a(n) = A279278(A000292(n)).
%e A298857 a(5) = 2 because fifth tetrahedral number is 35 and we have [35] and [20, 10, 4, 1].
%t A298857 Table[SeriesCoefficient[Product[1 + x^(k (k + 1) (k + 2)/6), {k, 1, n}], {x, 0, n (n + 1) (n + 2)/6}], {n, 0, 53}]
%Y A298857 Cf. A000292, A030273, A279278, A288126, A298269.
%K A298857 nonn
%O A298857 0,6
%A A298857 _Ilya Gutkovskiy_, Jan 27 2018