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%I #5 Dec 29 2018 14:32:49
%S 1,1,1,1,1,1,1,2,3,4,5,6,7,8,10,13,17,22,28,35,43,53,67,85,108,137,
%T 173,217,271,340,428,540,682,861,1085,1364,1714,2155,2712,3416,4305,
%U 5425,6832,8599,10821,13618,17142,21584,27182,34231,43102,54264,68311,85994
%N Number of compositions (ordered partitions) of n into hexagonal pyramidal numbers (A002412).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexagonalPyramidalNumber.html">Hexagonal Pyramidal Number</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)*(4*k-1)/6)).
%t nmax = 53; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1) (4 k - 1)/6), {k, 1, nmax}]), {x, 0, nmax}], x]
%Y Cf. A002412, A279222, A282582, A322340, A322798, A322802, A322853, A322855, A322856.
%K nonn
%O 0,8
%A _Ilya Gutkovskiy_, Dec 29 2018
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