|
%I #4 Jan 28 2018 11:02:12
%S 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 368,478,810,1055,1508,1778,2277,3815,5214,7103,8615,11614,18079,
%U 24428,33704,42877,56639,85597,116984,159179,199356,268965,400612,545674,740356,950897,1261597,1842307
%N Number of partitions of the n-th tetrahedral number into distinct 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/Par#part">Index entries for related partition-counting sequences</a>
%F a(n) = [x^A000292(n)] Product_{k>=1} (1 + x^A000292(k)).
%F a(n) = A279278(A000292(n)).
%e a(5) = 2 because fifth tetrahedral number is 35 and we have [35] and [20, 10, 4, 1].
%t 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 Cf. A000292, A030273, A279278, A288126, A298269.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Jan 27 2018
|
