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%I #5 Dec 22 2017 03:17:54
%S 0,1,2,4,11,47,292,2368,23427,272263,3628872,54525252,911484163,
%T 16775498551,337021458884,7338279413680,172130372061035,
%U 4327036966579151,116046966039565672,3307263639537314116
%N Partial sums of A029768.
%C Partial sums of number of increasing mobiles with n elements. In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root. The subsequence of primes in this partial sum begins: 2, 11, 47, 272263.
%H Robert Israel, <a href="/A174632/b174632.txt">Table of n, a(n) for n = 0..416</a>
%F a(n) = SUM[i=o..n] A029768(i).
%e a(x) = 0 + 1 + 1 + 2 + 7 + 36 + 245 + 2076 + 21059 + 248836 = 272263 is prime.
%p S:= rhs(dsolve({diff(a(x), x) = log(1/(1-a(x)))+1, a(0)=0}, a(x), series, order=31)):
%p L:= [seq(coeff(S, x, j)*j!, j=0..30)]:
%p ListTools:-PartialSums(L); # _Robert Israel_, Dec 21 2017
%Y Cf. A029768, A032220, A038037, A055356.
%K nonn
%O 0,3
%A _Jonathan Vos Post_, Mar 24 2010