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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.
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%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