A174432 - OEIS

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

%S 1,2,6,33,281,3111,41343,635202,11036914,213638812,4555901812,

%T 106107724162,2679887230354,72962091956750,2130453028323070,

%U 66421485491085025,2202438789394598209,77400308039913410963

%N Partial sums of A000699.

%C Partial sums of number of irreducible diagrams (in the sense of perturbation expansion in quantum field theory: spinor case in 4 spacetime dimensions) with 2n nodes. The subsequence of primes in this partial sum begins: 2, 281, and there never seem to be any more, as the underlying sequence is all even after A000699(8).

%F a(n) = SUM[i=1..n] A000699(i), where those A000699(n) = (n-1)*SUM[i=1..n-1] A000699(i)*A000699(n-i).

%e a(18) = 1 + 1 + 4 + 27 + 248 + 2830 + 38232 + 593859 + 10401712 + 202601898 + 4342263000 + 101551822350 + 2573779506192 + 70282204726396 + 2057490936366320 + 64291032462761955 + 2136017303903513184 + 75197869250518812754.

%Y Cf. A000699, A004300, A051862.

%K easy,nonn

%O 1,2

%A _Jonathan Vos Post_, Mar 19 2010