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%I #12 Apr 04 2015 02:42:27
%S 1,0,1,4,1,4,1,8,19,8,19,12,37,12,55,112,73,112,91,212,127,308,145,
%T 504,781,600,817,892,1453,1084,2089,1472,3343,1760,4579,6564,6433,
%U 6948,8287,11944,11341,16744,14395,26156,18667,35468,22921,53712,64273,67440
%N Total number of parts in all compositions of n into distinct odd parts.
%H Alois P. Heinz, <a href="/A097936/b097936.txt">Table of n, a(n) for n = 1..1000</a>
%F Sum_{k>0} (k*k!*x^(k^2)/Product_{j=1..k} (1-x^(2*j))).
%p b:= proc(n, i) option remember; `if`(n=0, 1,
%p `if`(n>(i+1)^2/4, [][], zip((x, y)->x+y, [b(n, i-2)],
%p `if`(i>n, [], [0, b(n-i, i-2)]), 0)[]))
%p end:
%p a:= proc(n) option remember; local l; l:=[b(n, n-1+irem(n,2))];
%p add(i*l[i+1]*i!, i=1..nops(l)-1)
%p end:
%p seq (a(n), n=1..60); # _Alois P. Heinz_, Nov 20 2012
%t Drop[ CoefficientList[ Series[Sum[k*k!*x^k^2/Product[1 - x^(2j), {j, 1, k}], {k, 1, 55}], {x, 0, 50}], x], 1] (* _Robert G. Wilson v_, Sep 08 2004 *)
%Y Cf. A097910, A079499, A032021.
%K easy,nonn
%O 1,4
%A _Vladeta Jovovic_, Sep 05 2004
%E More terms from _Robert G. Wilson v_, Sep 08 2004
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