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A282866
Expansion of Product_{k>=1} (1 + k^2*x^(k^2)).
1
1, 1, 0, 0, 4, 4, 0, 0, 0, 9, 9, 0, 0, 36, 36, 0, 16, 16, 0, 0, 64, 64, 0, 0, 0, 169, 169, 0, 0, 676, 676, 0, 0, 0, 225, 225, 36, 36, 900, 900, 144, 544, 400, 0, 0, 1924, 1924, 0, 0, 1345, 4945, 3600, 576, 772, 14596, 14400, 2304, 2304, 441, 441, 0, 6084, 7848, 1764, 64, 25184, 25120, 0, 256, 3392, 11236, 8100, 0, 576
OFFSET
0,5
COMMENTS
Sum of products of terms in all partitions of n into distinct squares (A000290).
FORMULA
G.f.: Product_{k>=1} (1 + k^2*x^(k^2)).
EXAMPLE
a(41) = 544 because we have [36, 4, 1], [25, 16], 36*4*1 = 144, 25*16 = 400 and 144 + 400 = 544.
MATHEMATICA
nmax = 73; CoefficientList[Series[Product[1 + k^2 x^k^2, {k, 1, nmax}], {x, 0, nmax}], x]
PROG
(PARI) Vec(prod(k=1, 73, (1 + k^2*x^(k^2))) + O(x^73)) \\ Indranil Ghosh, Mar 15 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 23 2017
STATUS
approved