%I #2 Mar 30 2012 18:40:51

%S 1,3,7,16,36,87,212,541,1403,3714,9931,26880,73230,200944,554216,

%T 1535969,4273508,11933297,33425583,93891713,264401743,746269426,

%U 2110694255,5981068081,16977958318,48271041858

%N Partial sums of A002861.

%C Partial sums of number of connected functions (or mapping patterns) on n unlabeled points, or number of rings and branches with n edges. The subsequence of primes in this partial sum begins: 3, 7, 9931, 1535969, 5981068081.

%F a(n) = SUM[i=1..n] A002861(i).

%e a(26) = 1 + 2 + 4 + 9 + 20 + 51 + 125 + 329 + 862 + 2311 + 6217 + 16949 + 46350 + 127714 + 353272 + 981753 + 2737539 + 7659789 + 21492286 + 60466130 + 170510030 + 481867683 + 1364424829 + 3870373826 + 10996890237 + 31293083540.

%Y Cf. A002861, A000081, A001372.

%K nonn

%O 1,2

%A _Jonathan Vos Post_, Feb 23 2010