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%I #21 Feb 21 2017 02:38:19
%S 0,0,2,5,16,27,59,96,164,260,415,606,923,1336,1911,2698,3787,5203,
%T 7142,9646,12962,17295,22902,30063,39315,51104,66013,84898,108658,
%U 138397,175593,221872,279207,350248,437607,545093,676764,837873,1033961,1272730,1562137
%N Sum of all parts that are not the smallest part (counted with multiplicity) of all partitions of n.
%H Alois P. Heinz, <a href="/A213359/b213359.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A066186(n) - A092309(n).
%F G.f.: Sum_{i>0}(x^i/(1-x^i))(Sum_{j>i}(j*x^j/(1-x^j))/Product_{j>i}(1-x^j)) (obtained by logarithmic differentiation of the bivariate g.f. given in A268189). - _Emeric Deutsch_, Feb 02 2016
%e a(4) = 5 because the partitions of 4 are [1,1,1,1], [1,1,2], [1,3], [2,2], and [4], having sum of parts that are not the smallest 0, 2, 3, 0, and 0, respectively, and 0 + 2 + 3 + 0 + 0 = 5. - _Emeric Deutsch_, Feb 02 2016
%p g := add(x^i*add(j*x^j/(1-x^j), j = i+1 .. 80)/((1-x^i)*mul(1-x^j, j = i+1 .. 80)), i = 1 .. 80): gser := series(g, x = 0, 55): seq(coeff(gser, x, n), n = 1 .. 40); # _Emeric Deutsch_, Feb 02 2016
%t max = 42; gser = Sum[x^i*Sum[j*x^j/(1-x^j), {j, i+1, max}]/((1-x^i)* Product[1-x^j, {j, i+1, max}]), {i, 1, max}]+O[x]^max; CoefficientList[ gser, x] // Rest (* _Jean-François Alcover_, Feb 21 2017, after _Emeric Deutsch_ *)
%Y Cf. A066186, A092269, A092309, A268189.
%K nonn
%O 1,3
%A _Omar E. Pol_, Jan 08 2013
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