%I A117455
%S A117455 0,0,1,2,4,8,12,19,27,41,54,76,99,133,171,223,279,357,443,554,682,841,
%T A117455 1022,1247,1504,1814,2174,2603,3092,3676,4346,5127,6030,7076,8275,9669,
%U A117455 11254,13078,15167,17556,20270,23377,26899,30902,35448,40592,46403
%N A117455 Sum of the differences between the largest part and smallest part over 
               all partitions of n into distinct parts.
%C A117455 a(n)=sum(k*A117454(n,k),k=0..n-2).
%F A117455 G.f.=sum(x^(i(i+1)/2)*sum(1/(1-x^j), j=1..i-1)/product(1-x^j, j=1..i), 
               i=1..infinity) (obtained by taking the derivative with respect to 
               t of the g.f. G(t,x) of A117454 and letting t=1).
%e A117455 a(7)=12 because the partitions of 7 into distinct parts are [7],[6,1],
               [5,2],[4,3] and [4,2,1] and (7-7)+(6-1)+(5-2)+(4-3)+(4-1)=12.
%p A117455 g:=sum(x^(i*(i+1)/2)*sum(1/(1-x^j),j=1..i-1)/product(1-x^j,j=1..i),i=1..15): 
               gser:=series(g,x=0,55): seq(coeff(gser,x^n),n=1..50);
%Y A117455 Cf. A117454.
%Y A117455 Sequence in context: A125606 A136184 A011908 this_sequence A110571 A049696 
               A127405
%Y A117455 Adjacent sequences: A117452 A117453 A117454 this_sequence A117456 A117457 
               A117458
%K A117455 nonn
%O A117455 1,4
%A A117455 Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 18 2006