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A264395
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Number of Mersenne number parts in all partitions of n.
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1
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0, 1, 2, 5, 8, 14, 23, 37, 55, 84, 121, 175, 247, 346, 476, 654, 881, 1184, 1574, 2081, 2725, 3559, 4605, 5939, 7610, 9713, 12327, 15598, 19631, 24633, 30780, 38342, 47577, 58884, 72615, 89324, 109539, 133998, 163455, 198949, 241505, 292550, 353547, 426394
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OFFSET
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0,3
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COMMENTS
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a(n) = Sum_{k=0..n} k*A264394(n,k).
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LINKS
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FORMULA
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G.f.: ( Sum_{i>0} x^(h(i))/(1-x^(h(i)) ) / ( Product_{i>0} 1-x^i ), where h(i) = 2^i - 1.
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EXAMPLE
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a(4) = 8 because the partitions of 4 are [4], [3',1'], [2,2], [2,1',1'], [1',1',1',1'], where the Mersenne number parts are marked.
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MAPLE
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h := proc (i) options operator, arrow: 2^i-1 end proc: g := (sum(x^h(i)/(1-x^h(i)), i = 1..31))/(product(1-x^i, i = 1..100)); hser := series(g, x = 0, 55): seq(coeff(hser, x, n), n = 0 .. 50);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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