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Partial sums of A000272.
0

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

%S 1,2,3,6,22,147,1443,18250,280394,5063363,105063363,2463011054,

%T 64380375278,1856540769315,58550453144611,2004745521503986,

%U 74062339559431922,2936485391069247715,124376016487663499491

%N Partial sums of A000272.

%C Partial sums of number of trees on n labeled nodes. The subsequence of primes in this sequence begin: 2, 58550453144611, no more through a(30).

%F a(n) = SUM[i=0..n] A000272(i) = SUM[i=0..n] i^(i-2).

%e a(19) = 1 + 1 + 1 + 3 + 16 + 125 + 1296 + 16807 + 262144 + 4782969 + 100000000 + 2357947691 + 61917364224 + 1792160394037 + 56693912375296 + 1946195068359375 + 72057594037927936 + 2862423051509815793 + 121439531096594251776 + 5480386857784802185939.

%Y Cf. A000055, A000169, A000312, A007778, A007830, A008785-A008791, A033842, A000272, A036361, A036362, A036506, A000055, A054581, A097170

%K easy,nonn

%O 0,2

%A _Jonathan Vos Post_, Feb 13 2010