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%I #9 Nov 13 2015 16:19:20
%S 0,1,2,5,8,14,23,37,55,84,121,175,247,346,476,654,881,1184,1574,2081,
%T 2725,3559,4605,5939,7610,9713,12327,15598,19631,24633,30780,38342,
%U 47577,58884,72615,89324,109539,133998,163455,198949,241505,292550,353547,426394
%N Number of Mersenne number parts in all partitions of n.
%C a(n) = Sum_{k=0..n} k*A264394(n,k).
%F G.f.: ( Sum_{i>0} x^(h(i))/(1-x^(h(i)) ) / ( Product_{i>0} 1-x^i ), where h(i) = 2^i - 1.
%e 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.
%p 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);
%Y Cf. A000225, A264394.
%K nonn
%O 0,3
%A _Emeric Deutsch_, Nov 13 2015
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