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%I #5 Jan 15 2017 11:45:11
%S 1,1,0,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,0,1,1,1,1,1,
%T 1,1,1,0,0,0,0,1,1,0,0,1,2,1,0,0,2,2,0,0,1,1,1,1,0,0,2,2,0,0,2,3,1,0,
%U 1,2,1,0,0,0,1,2,1,1,2,2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,2,3,2,1,2,3,1,0,0,1,2
%N Expansion of Product_{k>=0} (1 + x^(3*k*(k+1)/2+1)).
%C Number of partitions of n into distinct centered triangular numbers (A005448).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CenteredTriangularNumber.html">Centered Triangular Number</a>
%H <a href="/index/Ce#CENTRALCUBE">Index entries for sequences related to centered polygonal numbers</a>
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=0} (1 + x^(3*k*(k+1)/2+1)).
%e a(46) = 2 because we have [46] and [31, 10, 4, 1].
%t nmax = 105; CoefficientList[Series[Product[1 + x^(3 k (k + 1)/2 + 1), {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A005448, A024940, A279278, A280950, A281082, A281083, A281084.
%K nonn
%O 0,47
%A _Ilya Gutkovskiy_, Jan 14 2017
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