%I #16 Dec 01 2013 13:35:01
%S 2,6,16,32,64,132,224,404,704,1156,1880,3060,4748,7396,11346,17054,
%T 25454,37706,54980,79756,114702,163394,231288,325408,454138,630542,
%U 870504,1194536,1631196,2216992,2997542,4036022,5411108,7223636
%N Sum of all parts of the n-th subshell of the head of the last section of the set of partitions of any even integer >= 2n.
%C The last section of the set of partitions of 2n contains n subshells.
%C Also first differences of A182736. - Omar E. Pol, Mar 03 2011
%F a(1) = 2. a(n) = A138880(2n) - A138880(2n-2), n >= 2.
%e a(5)=64 because the 5th subshell of the head of the last section of any even integer >= 10 looks like this:
%e (10 . . . . . . . . . )
%e ( 5 . . . . 5 . . . . )
%e ( 6 . . . . . 4 . . . )
%e ( 7 . . . . . . 3 . . )
%e ( 4 . . . 3 . . 3 . . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e . (2 . )
%e There are 17 parts whose sum is 10+5+5+6+4+7+3+4+3+3+2+2+2+2+2+2+2 = 10*5 + 2*7 = 64, so a(5)=64.
%Y Cf. A135010, A138880, A182736, A182742, A182982, A182992, A182995.
%K nonn
%O 1,1
%A _Omar E. Pol_, Feb 06 2011
%E More terms from Omar E. Pol, Mar 03 2011