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%I #4 Aug 15 2017 20:37:48
%S 1,1,1,1,0,1,1,2,2,1,1,0,2,2,2,3,1,2,2,2,3,2,4,3,3,3,2,5,4,5,4,2,3,3,
%T 6,6,5,5,4,5,7,8,8,7,6,6,6,8,9,9,9,7,8,9,9,11,10,11,11,10,12,10,14,15,
%U 14,14,11,13,13,17,17,14,15,14,17,20,19,20,20,20,21,20,21,21,25,26,23,22,21,24,27
%N Number of partitions of n into distinct generalized pentagonal numbers (A001318).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=1} (1 + x^(k*(3*k-1)/2))*(1 + x^(k*(3*k+1)/2)).
%e a(15) = 3 because we have [15], [12, 2, 1] and [7, 5, 2, 1].
%t nmax = 90; CoefficientList[Series[Product[(1 + x^(k (3 k - 1)/2)) (1 + x^(k (3 k + 1)/2)), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A000009, A001318, A095699, A218379, A218380, A279221, A280952, A281083.
%K nonn
%O 0,8
%A _Ilya Gutkovskiy_, Aug 14 2017
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